Abstract In this paper, the distributed dislocation technique (DDT) is developed to be utilized for the analysis of a cracked functionally graded piezoelectric-€“piezomagnetic (FGPP) layer under anti-plane mechanical and in-plane electric and magnetic fields. By using the Fourier transformation, the closed-form expressions for the shear stress, electric displacement and magnetic displacement components are obtained for a generalized Volterra-type screw dislocation. The generalized dislocation in FGPP layer contains dislocation in the displacement component and jump in the electric and magnetic potentials. The expressions of generalized stress intensity factor are derived in the DDT. The solution of the dislocation problem is utilized in the DDT to solve the problem of arbitrary configurations of multiple embedded and edge cracks. The generalized intensity factors of the cracked layer are obtained. Numerical results for generalized intensity factors of straight and curved cracks are presented. The DDT is proved to be useful in the analysis of the interaction of the embedded and edge cracks in an FGPP layer.