The problem of collision between spherical impactor and thin-walled containment involves geometrical multi-scale – shell thickness and impactor radius, specifically, 2 mm and 6 mm, are of two orders smaller than shell radius equal to 150 mm. Good spatial resolution for impactor and shell is required as their interfaces deformation is an object of investigation. Uniform meshes with a desirable spatial resolution become computationally impractical due to huge cells number. In order to overcome this difficultly we use dynamically adaptive Cartesian meshes. Computational cells can be split or merged during the computational run accordingly to a user's criterion designed to keep good spatial resolution only at sufficient domains of the flow. The usage of adaptive mesh refinement allows to achieve high accuracy of the numerical simulation in a smaller physical time. We discuss some issues on the usage of adaptive meshes for considered impact problem and present load balancing algorithm for distributed memory parallel calculations.