Abstract The fracture problem for a medium composed of a cracked piezoelectric strip with functionally graded orthotropic coating is studied. The layer is subjected to anti-plane mechanical and in-plane electrical loading. In this paper, we first address, the problem of a screw dislocation located in a substrate which is imperfectly bonded to the coating. Then, in order to model the cracked piezoelectric layer, by means of the dislocation solution, we construct integral equations for the layer, in which the unknown variables are dislocation densities. These unknowns are determined through satisfaction of the boundary conditions on the crack faces. By use of the dislocation densities, the field intensity factors are determined. Several examples are presented to demonstrate the applicability of the proposed solution. ", keywords = Piezoelectric strip; Functionally graded layer; Imperfect bonding; Multiple cracks; Stress intensity factors, isbn = 0020-7403, doi=https://doi.org/10.1016/j.ijmecsci.2014.11.025