We present an interactive algorithm to model physics-based interactions in multi-agent simulations. Our approach is capable of modeling both physical forces and interactions between agents and obstacles, while allowing the agents to anticipate and avoid collisions for local navigation. We combine velocity-based collision-avoidance algorithms with external physical forces. The overall formulation can approximately simulate various physical effects, including collisions, pushing, deceleration and resistive forces. We have integrated our approach with an open-source physics engine and use the resulting system to model plausible behaviors of and interactions among large numbers of agents in dense environments. Our algorithm can simulate a few thousand agents at interactive rates and can generate many emergent behaviors. The overall approach is useful for interactive applications that require plausible physical behavior, including games and virtual worlds.