A new method for modeling contact in the material point method (MPM) is developed. This new approach uses the displacement field to create surfaces that identify regions where contact, including self-contact, may occur. The nodal basis functions of MPM are modified based on these surfaces to ensure that contributions are only made to material points with similar displacements. This partitioning between the grid nodes and material points does not require that the materials points have a priori material coloring or surface indicators and therefore avoids the need to have separate velocity fields for different materials or the need to separately track and evolve contact surfaces. Furthermore, the contact algorithm developed here does not assume or modify material properties near the contact surface. Numerical simulations of several contact problems using this approach are presented.