The proximal Galerkin method is a numerical method for solving variational problems with inequality constraints [1]. We apply the method to Signorini’s problem, the classical model of a three-dimensional linearly elastic body resting on a rigid, frictionless surface, and multi-body contact problems. We also introduce a regularized primal form of proximal Galerkin and provide implementations using the finite element software MFEM [2]. [1] Jørgen S. Dokken and Patrick E. Farrell and Brendan Keith and Ioannis P.A. Papadopoulos and Thomas M. Surowiec, The latent variable proximal point algorithm for variational problems with inequality constraints, Computer Methods in Applied Mechanics and Engineering, Vol. 445, pp. 118181, 2025 [2] R. Anderson and J. Andrej and A. Barker and J. Bramwell and J.-S. Camier and J. Cerveny and V. Dobrev and Y. Dudouit and A. Fisher and Tz. Kolev and W. Pazner and M. Stowell and V. Tomov and I. Akkerman and J. Dahm and D. Medina and S. Zampini, MFEM: A Modular Finite Element Methods Library, Computers & Mathematics with Applications, Vol. 81, pp. 42-74, 2021