The results of numerical investigation of the processes of dynamic deformation of composite cylindrical shell protected inside with a cylindrically rolled packet of metallic woven grids are presented. Internal loading is achieved through the explosion of spherical charge. Mathematical model of metallic grids deformation suggested earlier is now provided with experimental diagram of dynamic compression in the direction perpendicular to the grid layers. In circumferential direction the value of effective elastic modulus is selected in series of calculations. Estimated data is compared with the experimental results. The existence of the gas-permeable cylindrical packet of grids leads to decrease of maximum circumferential deformation of the outer shell.