An extension to solid mechanics of the FLIP particle-in-cell method is presented. The particle-in-cell method uses two representations of the continuum,one based on a collection of material points and the other based on a computational grid. The material points are followed throughout the deformation of a solid and provide a Lagrangian description that is not subject to mesh tangling. This feature permits constitutive equations with history-dependent variables to be applied at these material points with no requirement for mapping the history parameters from one point to another. A grid, which can be held fixed or adapted as the need arises, is used to determine spatial gradients. Since the grid is used as an updated Lagrangian frame, the nonlinear convection term associated with Eulerian formulations does not appear. With the use of maps between material points and he grid, the advantages of both Eulerian and Lagrangian schemes are utilized. No-slip impact between bodies, inelastic, elastic, or rigid, is handled automatically by the method without resorting to a special contact algorithm.