We present an explicit numerical method for three-dimensional modeling of fast processes of fluid structure interaction problems in Euler variables. The method does not require complex spatial grid generation. To set the initial geometry and follow the deformation of the calculating domains in the process of interaction it is enough to take into account the interacting surfaces constituted by a set of triangles created by CAD systems. The method is based on the modified Godunov scheme with the increased accuracy and uniform for solving equations of fluid dynamics and elastic-plastic flows. Fixed Cartesian grid and local mobile grids associated with each triangle of the surface are used. The flow parameters are interpolated from the Cartesian grid to the local grids and vice versa. At the fluid structure interaction boundary the exact Riemann solver is used.