The problem of high-velocity impact was modeled on the basis of two numerical methods, the smoothed particle hydrodynamics (SPH) and the Eulerian total variation diminishing (TVD) finite-difference scheme. The modification of SPH method was elaborated. In this modification, the summation approach and the continuous approach are equivalent, and the problem of boundary particle deficiency is successfully resolved. The comparison of modified SPH and Eulerian finite-difference approaches shows a good agreement between them. The calculations results can be useful for estimation of efficiency of anti-meteorite protection shields, giving information on the shape and size of formed apertures and jets. (C) 2012 Elsevier Ltd. All rights reserved.