Abstract: The large-scale mechanical behavior of woven cloth is determined by the mechanical properties of the yarns, the weave pattern, and frictional contact between yarns. Using standard simulation methods for elastic rod models and yarn-yarn contact handling, the simulation of woven garments at realistic yarn densities is deemed intractable. This paper introduces an efficient solution for simulating woven cloth at the yarn level. Central to our solution is a novel discretization of interlaced yarns based on yarn crossings and yarn sliding, which allows modeling yarn-yarn contact implicitly, avoiding contact handling at yarn crossings altogether. Combined with models for internal yarn forces and inter-yarn frictional contact, as well as a massively parallel solver, we are able to simulate garments with hundreds of thousands of yarn crossings at practical frame-rates on a desktop machine, showing combinations of large-scale and fine-scale effects induced by yarn-level mechanics.