AbstractDespite great strides in past years are being made to generate motions of elastic materials such as cloth and biological skin in virtual world, unfortunately, the computational cost of realistic high‐resolution simulations currently precludes their use in interactive applications. Thin elastic materials such as cloth and biological skin often exhibit complex nonlinear elastic behaviors. However, modeling elastic nonlinearity can be computationally expensive and numerically unstable, imposing significant challenges for their use in interactive applications. This paper presents a novel simulation framework for simulating realistic material behaviors with interactive frame rate. Central to the framework is the use of a constraint‐based multi‐resolution solver for efficient and robust modeling of the material nonlinearity. We extend a strain‐limiting method to work on deformation gradients of triangulated surface models in three‐dimensional space with a novel data structure. The simulation framework utilizes an iterative nonlinear Gauss–Seidel procedure and a multilevel hierarchy structure to achieve computational speedups. As material nonlinearity are generated by enforcing strain‐limiting constraints at a multilevel hierarchy, our simulation system can rapidly accelerate the convergence of the large constraint system with simultaneous enforcement of boundary conditions. The simplicity and efficiency of the framework makes simulations of highly realistic thin elastic materials substantially fast and is applicable of simulations for interactive applications. Copyright © 2015 John Wiley & Sons, Ltd.