The article describes numerical modeling detonation initiation in shielded thin layers of explosives exposed to high-speed projectiles with regard to their shock-wave desensitization occurring due to their pre-compression by the shock wave generated at the initial stage of projectile penetration in the shielded layer of explosive. In the course of solving the problem by using LS-DYNA it was found that due to lack of accountability of shock wave desensitization effect in Lee-Tarver kinetics, integrated into the program LS-DYNA, it is not possible to reproduce the experimental fact of existence of the maximum screen thickness, above which detonation of the charge PVV-12M, of 6 mm thick is not initiated when exposed to the projectile with the diameter of 17.5 mm, at the speed of 2.21 kmps. To account for the effect of shock wave desensitization in problems of detonation initiation two-dimensional numerical solver of problems of mechanics of compressible solid continuum "Erudit", developed by S. V. Fedorov in the BMSTU, was used. Modernized Lee-Tarver kinetics of explosive decomposition, regarding for the possibility of desensitization of explosives under non-monotonic loading, was integrated into this solver. The developed method of numerical simulation allows the experimental data to be reproduced. As the calculations showed the detonation initiation doesn't occur under the projectile influence on a shielded thin layer of PVV-12M mm with the thickness of 6 mm and a faceplate thickness of 7 mm, but at a thickness of 6 mm detonation initiation occurs, which is consistent with experimental data.