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We present physically based algorithms for interactive deformable shape and motion modeling. We coarsely sample the objects with simulation nodes, and apply a meshless finite element method to obtain realistic deformations at interactive frame rates. This shape deformation algorithm is then used to specify keyframe poses and a smooth interpolating motion is obtained by solving for an energy-minimizing trajectory. We show how to handle collisions between different deformable objects as well as with static or moving scene objects. Secondary motion is added as a post-process by running a meshless elastic solid simulation. We enforce precomputed trajectories using control forces computed using shape matching. Key to the efficiency of our method is a sparse deformation representation and an adaptive optimization algorithm that automatically introduces new degrees of freedom in problematic regions. An accurate temporal interpolation scheme that exactly recovers rigid motions keeps the number of unknowns low and achieves realistic deformations with very few keyframes. We also show how the algorithm allows combining purely physical simulation with keyframe-based scripted animation. The presented results illustrate that our framework can handle complex shapes at interactive rates, making it a valuable tool for animators to realistically model deformable 3D shapes and their motion.