The Wall Street Crash of 1929 was not really a cause of the Depression. It was just the catalyst that activated all the problems with the US economy.
We know that stock market crashes themselves don't cause depressions. We have had crashes since 1929 and none of them has caused a depression. This seems to indicate that a crash is not a cause of an economic downturn but rather a symptom.
Economists do not agree completely on the causes of the Great Depression. Some point to the fact that the big countries of the world were returning to a gold standard. This reduced the money supply and helped cause the Depression. Others say that firms in the US were producing too much and not paying their workers enough to consume it all. But no one argues that the Crash actually caused the Depression. As this link says,
the stock market collapse did not cause the depression.