Abstract: Alchian and Friedman consider that financial market should eliminate the irrational traders.This essayest ablishes a model adopt birth death process to research the stock market which have rational traders and irrational traders.We studies the velocity of rational traders and irrational traders enter and quit the stock market.Based on this we can analysis the dynamic rule of the increase or decrease of the numbers of rational traders and irrational traders in stock market.Our conclusion is that the irrational traders may not be eliminated from the stock market.Their survival or disappear depend on many factors which include the initial wealth of irrational traders,the profits and losses of irrational traders,etc.

Key words: stock market evolutionary, birth death process, rational traders, irrational traders