By ALE method simulates two-dimensional blood flow through a stenosis elastic artery and by the finite element method makes numerical simulation of the blood flow through a stenosis rigid artery. At the same boundary conditions，compares the varying situations of the flow velocities and pressures in the stenosis elastic artery and the rigid. The simulation results show that the velocity and pressure in the rigid artery are not stable with the extension of flow field and in the elastic artery, because of the flexiblility of the elastic wall, the changes of the velocity and pressure are apparently smaller and stabler, which is more similar to physiological situation. The simulation of rigid artery can not meet the case of normal physiological condition and the computing results are far from the actual condition, meanwile explains that the ALE method is practicable for the numerical research of blood flow in blood vessels.