In this paper, a new numerical algorithm based on the discrete element method is presented for analyzing the dynamic problems under impact loading. Based on the basic principle of continuum mechanics, a connective model for orthotropic media is derived using disk elements. It is also extended to a bilinear hardening elastic-plastic model for calculating the plastic deformation in metals. Moreover, Mohr-Coulomb type failure criterion is used to judge the failure of concrete, and a contact discrete model is added in the algorithm. So the algorithm can calculate not only the impact problems of continuum and non-continuum, but also the transient process from continuum to non-continuum. The wave propagation in orthotropic planes under impact loading is numerically simulated. Through comparing the results with those computed by other numerical methods and examining the stability of the numerical solution, the accuracy and efficiency of the algorithm are discussed. In addition, the transient respondences of a steel warhead penetrating a concrete disc harrow is simulated, and three kinds of basic damage forms of concrete disc harrow under different penetration velocities of warhead are summarized.