For the simulation of soil, the Non-Smooth Contact Dynamics Method (NSCD) has become a popular alternative to classical Discrete Element Methods. In NSCD a contact between two particles is modeled using a complementarity condition: Either the particles are in contact and a reaction must be enforced that keeps them from penetrating, or the contact is separating and no contact force is required. A configuration must be found where the complementarity conditions hold for all contacts simultaneously. Introducing friction leads to a conical complementarity problem that is hard to solve numerically. Yet, a frictional contact model is indispensable in soil mechanical simulations. Popular iterative methods for this class of problems are given by the projected Gauss-Seidel and Gauss-Jacobi schemes. They deliver results that are faithful to the eye, even when reaction forces are still far from the expected result. The convergence rate stalls quickly, which can be a problem in large scale simulations where the values of the reaction forces are of interest. Interior point methods (IPM), on the other hand, supply iterative schemes for complementarity problems that are known to converge superlinearly. We propose an IPM based on Jordan algebraic properties of cones, that is closely related to the one presented by Kojima et al for linear complementarity problems in 1991. The possibility of using such a method in soil mechanical simulations is discussed as well as some numerical implications.