This paper explores the intersection of emerging surface technologies, capable of sensing multiple contacts and often shape information, and advanced games physics engines. We define a technique for modeling the data sensed from such surfaces as input within a physics simulation. This affords the user the ability to interact with digital objects in ways analogous to manipulation of real objects. Our technique is capable of modeling both multiple contact points and more sophisticated shape information, such as the entire hand or other physical objects, and of mapping this user input to contact forces due to friction and collisions within the physics simulation. This enables a variety of fine-grained and casual interactions, supporting finger-based, whole-hand, and tangible input. We demonstrate how our technique can be used to add real-world dynamics to interactive surfaces such as a vision-based tabletop, creating a fluid and natural experience. Our approach hides from application developers many of the complexities inherent in using physics engines, allowing the creation of applications without preprogrammed interaction behavior or gesture recognition.