A model of a viscoelastic infinite half-space with a concentrated tangential force applied on the boundary, namely, the viscoelastic Cerruti’s problem, is presented in this paper, with the derivation of the stress distributions by applying the elastic-viscoelastic correspondence principle to the displacements from the classic Cerruti’s problem. In the background viscoelastic materials, based on elastic-viscoelastic correspondence principle, the displacements of the classic Cerruti’s problem should have the similar expressions to elastic solutions but vary with time. Two auxiliary functions were used to replace the time components in displacements, which reduces the complexity. By satisfying the boundary conditions and balance conditions, the two auxiliary functions can be determined after solving two Volterra integral equations. With displacements known, the strains and stresses can be obtained. The results were also show that the two solutions match.