In this study, dynamic fracture analysis of an interface crack between two dissimilar piezoelectric layers is investigated. The composite is subjected to uniformly anti-plane mechanical impacts and in-plane electric displacement impacts under permeable and impermeable boundary conditions. The integral transform, Cauchy singular integral equation methods, and Chebyshev polynomial expansions are applied to obtain the solutions in the Laplace transform domain. Durbin’s method is used to carry out the numerical inversion of Laplace transform. The accuracy of numerical results is examined and the applicable numerical parameters are suggested by the experience of calculation. Finally, the numerical results are evaluated and discussed in detail.