This paper presents a numerical technique for modeling elastic-wave propagation in media with discrete distributions of fractures. The scheme is developed following the explicit treatments of fractures based on a linear-slip displacement-discontinuity model instead of using an effective-medium theory. The algorithm is implemented on an irregular numerical mesh by using the proposed integral forms of the elastic-momentum equations and displacement-discontinuity conditions together with a triangular-grid finite-difference operator. As a result, arbitrary nonplanar fractures can be explicitly represented on the mesh without extra computational cost. In contrast to schemes based on effective-medium theory, no stability problem arises here when incorporating fractures with any fracture compliance. The proposed scheme allows the background medium to be heterogeneous and, furthermore, allows the medium to differ on both sides of the fracture. In comparison with the seismic response calculation in the background medium in the absence of the fractures, the additional computational cost and memory requirements for incorporating many fractures are small. Examples of seismic-wave scattering from single horizontal and tilted fractures as well as a set of parallel tilted fractures demonstrate the good behavior of the proposed algorithm.