Liquid crystal elastomers, sometimes called “artificial muscles,” combine the elastic properties of rubber with the molecular order properties of liquid crystals. These fascinating materials stretch, shrink, bend or flap in response to changes in temperature, illumination, or applied fields, due to strong coupling between orientational order and elastic strain. Their mechanical response under applied strain is also peculiar, showing in some geometries a pronounced plateau in the stress-strain curve, accompanied by formation of a striped microstructure with director rotation in alternating directions. We construct a mesoscale model of this system based on a simple free energy functional and implement it using finite element elastodynamics. Simulation studies reproduce the dynamic stripe instability along with the resulting soft elastic response; we model the mechanical behavior of both single domain and polydomain samples, and use simulations to explore possible device applications. Next we turn to coarse-grained simulation studies of lipid vesicles, another soft material where changes in orientational order and microstructure may induce shape change. We present preliminary results demonstrating a variety of mechanisms by which changes in microstructure induce spherical vesicles to elongate, flatten, bulge, bud, or break. Work supported by NSF-DMR-0605889.