The aim of the present paper is to study theoretically and numerically the Verlet scheme for the explicit time-integration of elastodynamic problems with a contact condition approximated by Nitsche’s method. This is a continuation of papers (Chouly et al. ESAIM Math Model Numer Anal 49(2), 481–502, 2015; Chouly et al. ESAIM Math Model Numer Anal 49(2), 503–528, 2015) where some implicit schemes (theta-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed and stable under appropriate conditions. A theoretical study of stability is carried out and then illustrated with both numerical experiments and numerical comparison to other existing discretizations of contact problems.