Cloth simulation is an important topic for many applications in computer graphics, animation, and augmented virtual reality. The mechanical behavior of cloth objects can be mod- eled by the Kirchhoff–Love thin shell equations, which lead to large-scale, nonlinear, ill-conditioned algebraic equations. We propose to solve these nonlinear problems efficiently using the recursive multilevel trust region (RMTR) method. Our multilevel framework for cloth simulations is based on Catmull–Clark subdivision surfaces, which facilitates generation of the mesh hierarchy and also provides the basis for the finite element discretization. The prolongation and restriction operators are similarly constructed based on the subdivision rules. Finally, we leverage a reverse subdivision operator to transfer iterates from fine levels to coarser levels. The novel use of this fine-to-coarse operator provides a computationally efficient alternative to the least-square approach used elsewhere. Using the resulting RMTR variant, we present numerical examples showing a reduction in the number of iterations by several orders of magnitude when compared to a single-level trust region method.