Summary This paper describes a method for doing cloth simulation using large time steps by way of an implicit integration system. This method is an improvement over other explicit methods that require very small time steps and even other implicit numerical methods used previously. Key Ideas 1. Simulation models cloth particles as a triangular using simple continuum formulation for the internal forces in the cloth. Modeling operations such as stretch, compression, and damping forces can be applied to these forces as well. 2. The implicit integration method used generates an unbanded, sparse linear system that is solved using a modified conjugate gradient method. This solver also has the property that it can enforce contraints on the cloth particles exactly, independent of the solver iterations, and thus is capable of achieving much faster performance. 3. Collisions between cloth and solid objects are handled by preventing cloth particles from interpenetrating solid objects. Stiff penalty forces are used for whenever a particle is near to or is detected to have passed through a cloth triangle. Contributions An implicit integration formulation that handles contact and geometric constraints in a direct fasion, an extremely fast iterative solution algorithm based on conjugate gradient.