Abstract: The problem considered here is the antiplane response of a nonhomogeneous composite material containing some cracks subjected to dynamic loadings. It is assumed that the composite material is orthotropic and all the material properties only depend on the co ordinate y (along the thickness direction). In the analysis, the elastic region is divided into a number of strips of infinite length. The material properties are taken to be constants for each strip. By utilizing the Laplace transform and Fourier transform technique, the general solutions for strips are derived. The complete solution of the entire elastic region is then obtained through introducing the mechanical boundary and strip interface conditions via the flexibility/stiffness matrix approach. Attention is focused on the time dependent full field solutions of stresses, stress intensity factor and strain energy release rate. As a numerical illustration, the dynamic stress intensity factor of a functionally graded material with two cracks under sudden applied forces on crack faces are presented for various material nonhomogeneity parameters.