This paper presents a method for resolving contact in dynamic simulations of articulated figures. It is intended for humanoids with polygonal feet and incorporates Coulomb friction exactly. The proposed technique is based on a constraint selection paradigm. Its implementation offers an exact mode which guarantees correct behavior, as well as an efficiency optimized mode which sacrifices accuracy for a tightly bounded computational burden, thus facilitating batch simulations or the use of highly detailed foot models. The method has been applied to the simulation of two humanoid robots, CB and Hoap-2, and validated with respect to human and robot motions recorded in reality and in simulation. The friction parameters of contact have also been established empirically.