Abstract: In this paper, a program is made using the 8-nodes isoparametric finite element method to study wave propagation problems ard its interaction with the underground structure of a two-dimensional space-time domain in geo-medium elastic plane strain computer code. When a discontinuity in the derivative of the load with respect to time occurs, in the finite element numerical computations for solving the above-mentioned wave propagation problems, it will generally lead to the so-called initial illness' and 'overshoot phenomenon'. In the finite element analysis for solving wave propagation problems, based on the variational principle and the wave motion theory, this paper analyzes the causes which account for the above occurrence. A method to improve the computational accuracy for numerical solution by considering the acceleration-discontinued characteristics has been given and discussed in detail. Several examples ara compared with theoretical solutions, the computational results are satisfactory.