The most conservative scholarship considers that the pharaoh of Egypt at the time of the Exodus (c. 1446 BC) was Amenhotep II (1450-1424 BC). The overwhelming biblical and historical evidence is that he did not die with his army in pursuit of Israel.
In Psalm 136:15, we find that God "overthrew Pharaoh and his army in the Red Sea." The Hebrew word translated here as "overthrew" is na'ar, also found in Exodus 14:27. It does not mean "to drown" or "to toss or tumble about as in the water" as some have attempted to assert. It simply means "shook off" as is mentioned in the margins of many Bibles and in the Brown, Driver & Briggs Hebrew Lexicon. (Nehemiah 5:13 illustrates how na'ar should be translated: "Then I shook out the fold of my garment. . . .") Therefore, these verses simply say that God shook off the Egyptians, including Pharaoh, from their pursuit of the Israelites. These scriptures say nothing of who was drowned.
In Exodus 14:28, the waters cover "all the army of Pharaoh," but Pharaoh himself is not mentioned. Exodus 15:19 supports this: "For the horses of Pharaoh went with his chariots and his horsemen into the sea, and the LORD brought back the waters of the sea upon them." Naturally, the horses and horsemen of Egypt were considered to be Pharaoh's. But this verse does not say that Pharaoh's personal horse, or that Pharaoh himself, drowned in the sea.
This is significant because the death of such an important person would almost certainly have been given special note in the Bible. The Old Testament contains many clear references to the deaths of enemy kings, most of them much less important than this pharaoh. Archaeology proves that Amenhotep II, if he is the Pharaoh of the Exodus, ruled for about 22 more years.