While there has been significant progress in simulating collisions between rigid bodies, much remains to be done for modeling interactions between soft bodies. Graphical techniques for representing and deforming soft bodies range from non-physical (e.g., control point-based) to physically plausible (e.g., FFD) to physically realistic (e.g., FEM). All of these techniques require three operations to model interactions between soft bodies: 1) detecting collisions between deforming bodies, 2) computing impact forces when bodies collide, and 3) determining deformation forces or contact deformation of the bodies to initialize a deformation technique. In this report, we propose a new framework which performs all three operations quickly, with efficient use of memory, and more accurately than previous methods. The results of these operations can be used in any of the deformation techniques mentioned above.