In this paper some local properties of the solutions to nonsmooth variational inequalities are established. The perturbed solutions to the nonsmooth variational inequalities are shown to be locally Lipschitzian continuous in the ordinary or the generalized sense at the local solution points under certain regular conditions and/or generalized second-order sufficient conditions whether the constraints set is polyhedral or not. The conditions for ensuring the local uniqueness of the local solutions and the stationary points are also given in the nonpolyhedral casc