Simulating the mechanics of biological tissues entails a number of challenging requirements, including non-linear, anisotropic and nearly-incompressible materials, organic shapes with flat and thin structures, and large changes in shape such as bending twisting, bulging and stretching. To address these challenges, we are developing an open source dynamics simulator, ArtiSynth, that combines rigid body models with large-deformation finite-element models together with contact and constraints. In this talk, I will describe ArtiSynth’s mathematical framework within the context of the biological problem of simulating the muscle tissue structures found in tongues, tentacles and trunks.