This practice and experience paper describes a robust C++ implementation of several non-linear solid three-dimensional deformable object strategies commonly employed in computer graphics, named the Vega finite element method (FEM) simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint–Venant Kirchhoff FEM model, mass–spring system and invertible FEM models: neo-Hookean, Saint–Venant Kirchhoff and Mooney–Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modelling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.