Abstarct: Fracture and crack analysis is one of the most important branches of Solid Mechanics. In this research, the determination of strain release energy in cracked FGP materials is studied. The gradual variations of material properties are named as a special function (FGM). If these materials, however, have piezoelectric property too, then they are called FGP. In recent years in the fields of buckling, vibrations, fracture, stress analysis and electeromechanical and thermal forces of these materials have been widely studied. The numerical method used in this research, is the Galerkin element less method which was created by Blichko in 1994. This method is baxsed on the approximation of least square summation between several grids selected in the body and has some advantages to the common Finite Element methods. For instance, faster convergence, no need to meshing the body and the ability of the increasing the grids at any instant can be mentioned as its advantages. One of the most important capabilities of this method is its application in the analysis of fracture mechanics which is the subject of this research. The computer program is written in MATLAB. The crack considered here is in mode I. The plate is subjected to uniform distributed stress and uniform electrical displacement. In this research, the effects of distributed mechanical force and electrical displacement on the stress field, strain release energy, displacement and electrical field for the cases of homogenous uniform plate, simple piezoelectric plate and simple FGP plate and finally cracked FGP plate are studied. Also the program is run for four piezoceramic types with different values for geometry ratio and the effects of variation of material and geometry ratio are also investigated. The results show that when the geometry ratio is increased, the strain release energy is reduced. In FGP with no crack, by increasing the factor , the displacement, stress and electrical potential will increase.