It is a common charge from critics that the Exodus left no archeological evidence behind. The Christian answer, as “convenient” as it sounds to those critics, is pretty true if you actually put on your thinking cap for a moment.
In the words of Charlie Campbell:
Another objection critics raise regarding the Exodus concerns the lack of any Egyptian records mentioning the Israelite’s departure from the land. But a lack of records should not concern us. It is reasonable to believe that the Egyptians had some written record of the Exodus but as British Egyptologist Kenneth A. Kitchen says, voluminous papyrus archives once stored in Egypt have vanished:
In the sopping wet mud of the Delta, no papyrus ever survives (whether it mentions fleeing Hebrews or not)…In other words, as the official thirteenth-century archives from the East Delta centers are 100 percent lost, we cannot expect to find mentions in them of the Hebrews or anybody else. 
“Well,” the skeptic says, “perhaps no written record survives on papyrus, but surely there should be something in a wall relief that mentions the Exodus.”
I disagree. As Jeffery Sheler, U. S. News & World Report religion writer, says:
Official records and inscriptions in the ancient Near East often were written to impress gods and potential enemies, it would be quite surprising to find an account of the destruction of pharaoh’s army immortalized on the walls of an Egyptian temple…Indeed, the absence of direct material evidence of an Israelite sojourn in Egypt is not as surprising, or as damaging to the Bible’s credibility, as it first might seem. 
“Okay,” the skeptic reasons, “perhaps there wouldn’t be a wall relief telling the story of the Exodus, but surely the Israelites would have left behind some pottery in the Sinai desert during their sojourn from Egypt to Canaan.”
When it comes to archaeological evidence for the Exodus (such as pottery), it is important to remember that the Israelites lived as nomads during their time in the wilderness. Nomads living in a desert like environment, where every utensil and tool is of great value, leave few traces in the archaeological record. The Israelite’s temporary tent encampments from 3000 years ago would not have left much behind in the swirling sands of the desert.
Former Yale professor Millar Burrows agrees: “It is hardly reasonable, in fact, to expect archeological evidence of their sojourn anywhere. We cannot expect much help from archeology in tracing the route of a people’s migration through the desert.” (source)
See this article for more detail. We wouldn’t expect much archelogical evidence to survive. Really, nomadic people leave very little behind. Check JP’s comparison to the Scythians in the article for information on that.
- K. A. Kitchen, On the Reliability of the Old Testament, 466. Italics in original.
- Jeffery Sheler, Is The Bible True? 78.
- Millar Burrows, What Mean These Stones? 63.
Former Christian turned atheist DaGoodS (DGS) has compiled a list of eleven questions that he doesn’t think Christians can answer. I’ve decided to take him on, since I’m a sucker for questions that Christians supposedly can’t answer. Hopefully, DGS and I can learn something from each other.
What century did the Exodus occur?
Trying to chip away at the historicity of the biblical accounts here.
No one knows, actually. Few scholars actually completely discount the possibility of the Exodus; in other words, most believe that it probably happened but we’re unsure of the exact date. James Cameron and Simcha Jacobovici, who previously tried to trash Christianity with the Jesus Tomb documentary, came out with Exodus Decoded, wherein they lay out a case for a historical Exodus.
Like the Jesus Tomb fiasco, this documentary is laden with evidence that supports their conclusion. Rather than explored or refuted, contradictory evidence is swept under the rug. They wish to make only their case, and try the case in the court of public opinion where an impressive TV special is all it will take to convince most people that you’ve got something.
So, here’s the rub: if the archeologists don’t know, then I’m happy saying that I don’t know, either. When more evidence comes to light, I’ll be happy to conclude something then.