For solving three-dimensional structural inverse gravimetry problem of finding the interface in multilayer medium, the linearized iterative gradient methods of steepest descent and minimal error with variable damping factors are proposed. On the base of Newton, Levenberg-Marquardt and linearized gradient methods, effective parallel algorithms for two- and three-layered media were implemented on the MVS-IMM parallel computing system, the Intel multi-core CPU and NVIDIA graphics processors of Supercomputer “Uran”. Research of parallel algorithms effectiveness and optimization was carried out. The parallel algorithms were incorporated into the developed remote computing service system “Specialized Web-Portal for Solving Geophysical Problems on Multiprocessing Computer Systems”. The model problem for three-layered media is solved.