Parallel algorithms of solving ill-conditioned systems of linear algebraic equations (SLAE) of big dimensions with noisy right hand side arising at the solving inverse geophysical problems are presented in this paper. The inverse problem is solved by modified S-approximation method which is one of variants of the linear integral representation method elaborated by academician of RAS V.N. Strakhov. The algorithm of block contrasting method (BCM) which is that separating the investigated area into subareas of most intensive anomalies is given in this paper. SLAE is solved by regularizated iterative three-layer Chebyshev method for each constructed subareas, and then the union of all obtained solutions is chosen as zero approximation for the whole system. The parallel algorithms are written with using MPI library. The efficiency and stability of the developed algorithms on the example of interpretation of the gravity data are presented.