The Pentateuch is suspected to have been written by four author's over a broad period of time according the JEDP theory: The Yahwish source (J), who used the name Yahweh when speaking of God, and the Elohist source (E) who used Elohim as God's name, wrote approximately between 1000-800BC; The Deuteronomist source (D) focused on centrallised worship and politics in around 600BC; and the Priestly source (P) who refers to God as Elohim and El-Shaddai around 500BC . Traditionally Moses is believed to have been the author but historically this does not seem accurate.
The reason I bring this up here is because the Exodus raises issues when considered in a historically factual sense and so it is important to see where the story originates. As far as archaeology can tell there is no clear evidence for a literal mass exodus of Jews from Egypt after years of slavery, yet many theories can loosely try to refer to it. The oppression of the Jews in Egypt and their deliverance from God to the promised land is a fundamental part of the Jewish tradition. For me it does not take away great significance to the meaning of the story if it did not truly happen, but this would not go down well with those belonging to the Abrahmic faiths. But if the Exodus did happen surely something a big as this would be recorded somewhere? True, the Egyptians are known to have covered up their failures and presented them as victories (Ramses and the Battle of Qadesh), and so it is possible that they would not have advertised such a humiliation; but the record of mass Jewish slavery surely would have required legal documentation somewhere?
A date for the Exodus has thus been impossible to conclude. It must have been at the earliest 1650BC as in 14:6 the king of Egypt 'had his chariot made ready and took his army with him' in pursuit of the Hebrews after they had fled - chariots were introduced to Egypt during the occupation of the Hyksos during the Second Intermediate Period of Egyptian history, and were not used before then. If this was the case then the author (of whom is likely one of the above mentioned between 1000-500BC) would be writing hundreds of years after. To complicate the date issue it is possible his retrospective narrating may be coloured by his own experiences and may not be historically accurate, assuming that the Egyptians had chariots at the time of this story... Nevertheless if we go with this idea, we are still left with a huge time span of possible dates and pharaohs - if this did indeed truly happen. The expulsion of the Hyksos, an Asiatic people who could be seen as the ancestors of the Israelites, may be interpreted as the origin of this story.
The Hyksos were not slaves to the Egyptians, and even ruled the North for a time. In some instances they were hired as workers for their foreign skills, but this cannot compare the slavery that goes with the Jewish story; they certainly didn't build any pyramids. But they were forced out of Egypt and Egypt was reunified after. If this is the origin of the story then I believe that the writers of Exodus had heard of this history and identified with the Hyksos people, re-writing the story for their own purposes.
It has also been suggested that this story is based even later and even more further from its narrative telling. As eventually written in Isiah, in the 6th Century BC the Israelites were under the dominion of the Babylonians and when Babylon fell, the Israelites were freed. The exodus could be a re-telling of this story of freedom; however, why would the Jews need two such stories?
As I am not a Biblical historian I shall leave the debate here, concluding that I do not believe the exodus happened literally as the Bible dictates and I believe it is a re-telling of old myths or historical happenings, modified to create a sense of identity for the Israelite people.