We consider the simulation of dense foams composed of microscopic bubbles, such as shaving cream and whipped cream. We represent foam not as a collection of discrete bubbles, but instead as a continuum. We employ the material point method (MPM) to discretize a hyperelastic constitutive relation augmented with the Herschel-Bulkleymodel of non-Newtonian viscoplastic flow, which is known to closely approximate foam behavior. Since large shearing flows in foam can produce poor distributions of material points, a typical MPM implementation can produce non-physical internal holes in the continuum. To address these artifacts, we introduce a particle resampling method for MPM. In addition, we introduce an explicit tearing model to prevent regions from shearing into artificially thin, honey-like threads. We evaluate our method's efficacy by simulating a number of dense foams, and we validate our method by comparing to real-world footage of foam.