(Note:  The answer to this question is taken directly from the book In the Beginning:  Compelling Evidence for Creation and the Flood by Walt Brown, PhD.  I consider this 325 page beautifully illustrated and well documented book to be the most scientific, well reasoned and comprehensive book concerning evidence for Creation and the Flood available. Excellent for home and/or Christian schools  You can find more information on this book here.

Many other questions will be answered if we focus on one question, “When did they live?” There are two common, but quite different, answers. Evolutionists say dinosaurs lived, died, and became extinct at least 60 million years before man evolved. Others believe God created all living things during the creation week. So man and dinosaurs lived at the same time. If we look at the evidence, sorting out these two very different answers should be easy. 

Did dinosaurs become extinct at least 60 million years before man evolved? Almost all textbooks that address the subject say so. Movies and television vividly portray this. One even hears it at Disney World and other amusement parks. Some will say that every educated person believes this. We frequently hear stories that begin with impressive-sounding phrases such as, “Two hundred million years ago, as dinosaurs ruled the earth, ...” But none of this is evidence; some of it is an appeal to authority.  (Evidence must be observable and verifiable.) 

Did man and dinosaurs live at the same time? Scientists in the former Soviet Union have reported a layer of rock containing more than 2,000 dinosaur footprints alongside tracks “resembling human footprints.”¹ Obviously, both types of footprints were made in mud or sand that has since hardened into rock. If they are human footprints, then man and dinosaurs lived at the same time. Similar discoveries have been made in Arizona.² If it were not for the theory of evolution, few would doubt that these were human footprints. 

The Book of Job is one of the oldest books ever written. In it, God tells Job of his greatness as Creator and describes an animal, called Behemoth, as follows: 

Behold now, Behemoth, which I made as well as you; He eats grass like an ox.  Behold now, his strength in his loins, And his power in the muscles of his belly. He bends his tail like a cedar; The sinews of his thighs are knit together. His bones are tubes of bronze; His limbs are like bars of iron.    (Job 40:15–18)

Marginal notes in most Bibles speculate that Behemoth was probably an elephant or a hippopotamus, but those animals have tails like ropes. Behemoth had a “tail like a cedar.” Any animal with a tail as huge and strong as a cedar tree is probably a dinosaur. Job 40:19–24 describes this giant, difficult-to-capture animal as not alarmed by a raging river. If the writer of Job knew of a dinosaur, then the evolution position is wrong, and man saw dinosaurs. 

The next chapter of Job describes another huge, fierce animal, a sea monster named Leviathan.³ It was not a whale or crocodile, because the Hebrew language had other words to describe such animals. Leviathan may be a plesiosaur (PLEE see uh sore), a large seagoing reptile that evolutionists say became extinct 60 million years before man evolved. 
Consider the many dragon legends. Most ancient cultures have stories or artwork of dragons that strongly resemble dinosaurs.⁴ The World Book Encyclopedia states that: 

The dragons of legend are strangely like actual creatures that have lived in the past. They are much like the great reptiles [dinosaurs] which inhabited the earth long before man is supposed to have appeared on earth. Dragons were generally evil and destructive. Every country had them in its mythology.⁵

The simplest and most obvious explanation for so many common descriptions of dragons from around the world is that man once knew the dinosaurs. 

What caused the extinction of dinosaurs? The flood. Because dinosaur bones are found among other fossils, dinosaurs must have been living when the flood began. There are dozens of other dinosaur extinction theories, but they all have recognized problems. Most of the food chain was buried in the flood. Therefore, many large dinosaurs that survived the flood probably had difficulty feeding themselves and became extinct. 

Were dinosaurs on the Ark? Yes. God told Noah to put representatives of every kind of land animal on the Ark. (Some dinosaurs were semiaquatic and could have survived outside the Ark.) But why put adult dinosaurs on the Ark? Young dinosaurs would take up less room, eat less, and be easier to manage. The purpose for having animals on board was so they could reproduce after the flood and repopulate the earth. Young dinosaurs would have more potential for reproduction than old dinosaurs. 

Most, if not all, dinosaurs hatched from eggs. The largest dinosaur eggs ever found were a foot long. Hatchlings, even after a year of growth while on the Ark, would be quite easy to handle. 

Possibly dinosaurs became very large, because they lived to great ages. Preflood humans could live for more than 900 years.  If whatever caused man to live so long had the same effect on dinosaurs, they could have grown very large. Reptiles, unlike other animals, continue to grow throughout their lives. Perhaps large dinosaurs, which are similar to reptiles in many ways, were just old. 

1 . Alexander Romashko, “Tracking Dinosaurs,” Moscow News, No. 24, 1983, p. 10.

2 . Paul O. Rosnau et al., “Are Human and Mammal Tracks Found Together with the Tracks of Dinosaurs in the Kayenta of Arizona?” Parts I and II, Creation Research Society Quarterly ; Vol. 26, September 1989, pp. 41–48 and December 1989, pp. 77–98.

Before 1986, many thought dinosaur tracks and human tracks were together along the banks of the Paluxy River in Texas. Some, but not necessarily all, of the humanlike tracks were apparently made by part of a dinosaur’s foot. A film, Footprints in Stone, and John Morris’ book, Tracking Those Incredible Dinosaurs, which popularized the man-track idea, have been withdrawn. A few creationists still claim that some of these manlike tracks were made by humans. I believe the Paluxy tracks should be studied more and many questions satisfactorily answered before claiming human tracks are along the Paluxy River. 

In Uzbekistan, 86 consecutive horse hoofprints were found beside supposedly 90 –100-million-year-old dinosaur tracks. Evolutionists have almost as much difficulty believing that horses and dinosaurs lived together as they do man and dinosaurs. Horses allegedly did not evolve until many millions of years after the dinosaurs became extinct. [See Y. Kruzhilin and V. Ovcharov, “A Horse from the Dinosaur Epoch?” Moskovskaya Pravda (Moscow Truth), 5 February 1984.] For a report of a quadruped that left hoof-shaped prints alongside 1,000 dinosaur prints, see Richard Monastersky, “A Walk along the Lakeshore, Dinosaur-Style,” Science News, Vol. 136, 8 July 1989, p. 21. 
3 . Leviathan is also mentioned in Psalms 74:14 and 104:26 and in Isaiah 27:1. Both Leviathan and Behemoth are described in the apocryphal book II Esdras. II Esdras 6:49–53 says these beasts were created on the fifth day and given separate territories because of their large size.
4. Lorella Rouster, “The Footprints of Dragons,” Creation Social Science and Humanities Quarterly, Fall 1978, pp. 23–28.

5 . Knox Wilson, “Dragon,” The World Book Encyclopedia, Vol. 5, 1973, p. 265.