An important question must be resolved regarding how to understand the phrase "two years after the flood" given in Genesis 11:10:
These are the generations of Shem: Shem was an hundred years old, and begat Arphaxad two years after the flood.
But first we need to determine the duration of the flood event from beginning to end. The beginning of the flood is linked to Noah's age in Genesis 7:11:
In the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, the same day were all the fountains of
the great deep broken up, and the windows of heaven were opened.
Similarly we find the end of the flood linked to Noah's age in Genesis 8:13-14:
And it came to pass in the six hundredth and first year, in the first month, the first day of the month, the waters were dried up from off
the earth: and Noah removed the covering of the ark, and looked, and, behold, the face of the ground was dry. And in the second month,
on the seven and twentieth day of the month, was the earth dried.
Thus we find the flood began when Noah was 600 years old, in the 2nd month, on the 17th day, and the flood ended when Noah was 601 years old, in the 2nd month, on the 27th day, hence the duration of the flood was 1 year and 10 days.
Given that the flood event latest for roughly 1 year, we need to figure out whether the phrase "two years after the flood" means two years after the beginning of the flood, or two years after the end of the flood. Not correctly understanding this could result in a one year error in the Bible calendar.
We can find the answer to this by looking at Genesis 9:28-29:
And Noah lived after the flood three hundred and fifty years. And all the days of Noah were nine hundred and fifty years: and he died.
Here we find that Noah lived after the flood 350 years, and the total age of Noah was 950 years. The Hebrew word for "after" used here in Genesis 9:28-29 is the same Hebrew word used in Genesis 11:10 (so we are comparing apples to apples).
First, let's assume that both "after" references mean after the end of the flood. To see if this is correct, recall that we found from Genesis 8:13-14 above, that Noah was 601 years old at the end of the flood. Now according to Genesis 9:28-29, Noah also lived 350 years after the flood, which would mean his total age would have been 601 years (age at end of flood) + 350 years (years lived after end of flood), for a total age of 951 years. We can see this does not agree with the 950 years total age we are told in Genesis 9:28-29. So it is not possible that the phrase "after the flood" is referring to after the end of the flood.
Now if we assume that "after" means after the beginning of the flood, we recall that Noah was 600 years old at the beginning of the flood (Genesis 7:11), and so if Noah lived an additional 350 years after the beginning of the flood (Genesis 9:28-29), then we find Noah's total age would be 950 years, which is in complete agreement with his lifespan given in Genesis 9:28-29.
Now we have a proper understanding of the phrase "two years after the flood" used in Genesis 11:10 to apply to the Bible calendar.