We present an efficient model based on finite elements for viscoelastic, highly flexible surfaces. It is particularly designed for numerically stiff materials such as textiles because it yields linear equations in each time step and allows fast time stepping in an implicit integration method. This is achieved by reducing the nonlinear elasticity problem to a planar, linear one in each step. We apply this model to a garment simulation in which we assemble garments from CAD cloth patterns, seam these together, and animate the cloth in dynamic scenes with any chosen material properties. This results in a physically accurate but also fast simulation.