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The paper presents a mathematical model and a parallel III-d code for modeling the collision process of molecular clouds. The formation of dense clamps that arise as a result of the collision of molecular clouds is a mechanism that allows one to explain the origin of new stars. These clamps are gravitational unstable objects by Jeans and are the precursors of new stars and star clusters. The modeling results of filamentary formations, i.e. concentrated areas with high gas density in molecular clouds (MC), and the non isothermic compression calculation data are discussed. The collision of molecular clouds can lead to initiation of star formation processes. Numerical experiments were carried out on grids using a different number of computational domain cells. In systematic calculations, grids consisting of 512 × 512 × 512 to 2048 × 1024 × 1024 cells were used. To speed up the calculation, we used specially developed code using OpenMP and CUDA parallel programming technologies. A simulation of the central and noncentral collisions of two MOs of different masses and the distribution of the initial density along the radius was carried out. The results of the interaction depend on a large number of factors: velocity, mass ratio, pulse direction, large-scale gas heterogeneity and other cloud parameters.