The shock premelting and spallation of single crystal copper under cylindrical converging impact are studied using molecular dynamics simulations. For the axis of a cylindrical potential wall along the [001] crystallographic direction, the anisotropy of shock response is very obvious at the shock strength 1.4 km s-1. Premelting occurs at the wavefront in the 110 direction, but not in the 100 direction. As a result of the converging effect, the requisite shock strength for generating premelting decreases in comparison with planar shock. Under th...