The results of mathematical modeling of slab collision processes arising from their tectonic movement are presented. Simulation is based on numerical solution of the solid mechanics equations by the finite element method using the MSC Marc code. All problems are solved in two-dimensional plane strain statement. Three models of processes are considered in detail: overthrusting fault of a deformable slab on a rigid slab; underthtrusting/subduction of a deformed slab under a rigid slab; formation of a day-surface relief in the vicinity of slabs collision. In the first two models, the overthrusting fault phenomenon and underthtrusting/subduction one are divided artificially to reduce mathematical difficulties, and in a latest model these phenomena are considered simultaneously. Satisfactory correspondence of modeling results with observable height of a ridge arch island (1~2 km) and the value of a deepwater trench (about 7 km) near the Kuril-Kamchatka subduction zone is obtained.

Key words: mathematical modeling, slabs collision, geodynamic processes.