Purpose In accord with the literature reviews, there is not a promising examination regarding the several straight and curved cracks interaction with arbitrary arrangement in the rectangular FGP plane. The purpose of this paper is to consider the effect of crack length, position of the point load, material non-homogeneity constant and also the arrangement of cracks on the resulting field intensity factors. Design/methodology/approach First of all, in order to obtain a set of Cauchy singular integral equations, both the dislocation method and the finite Fourier cosine transform technique are applied. Using the corresponding solution to these equations, the dislocation densities on the crack surfaces are then obtained. Considering the results, both the stress intensity factors (SIFs) and electric displacement intensity factors (EDIFs) for a vertical crack and the interaction between two straight and curved cracks, which have an arbitrary configuration, are determined. Findings The numerical examples are represented in order to illustrate the interesting mechanical and electrical coupling phenomena induced by multi-crack interactions. At the end, the effects of the material non-homogeneity constant, the crack length and the cracks arrangements on the SIFs and EDIFs are investigated. Originality/value The solutions are obtained in series expansion forms which may be considered as Green’s functions in an FGP rectangular plane possessing multiple cracks. The technique of Green’s function provides the ability to analyze multiple cracks having any smooth configuration.