Abstract: Aiming at the effects of rigid boundary condition, attenuation boundary condition and transmitting boundary condition on elastic wave field and the numerical frequency dispersion in calculation, the writers apply attenuation boundary condition and transmitting boundary condition as a mixed boundary one on artificial boundary, introduce mixed boundary condition into elastic wave numerical simulation, and adopt micro-damp in the caculation at the same time. The results prove that mixed boundary condition is better in absorbing the reflection of artificial boundary. Besides, the micro-damp method used in the calculation of numerical frequency dispersion can weaken the frequency dispersion caused by the division of grid and the computational error. This method can improve the precision effectively in the wave field simulation.