The analytical model to take into account the space charge of the beam on 3D rectangular mesh is implemented. The efficiency of the analytical model was studied by comparing the numerical integration, piecewise-constant & tri-linear analytical models with the exact solution for simple test problems. The singularity problems have been studied for different integration schemes. The adaptive integration scheme is suggested to increase the speed of calculations. The algorithms of analytical integration have been implemented in the POISSON-3D code devoted to simulation of high-current relativistic beam optics in 3D; Green’s function technique demonstrated its efficiency in the design of sheet-beam gun for SLAC X-band klystron.