We demonstrate a physically-based technique for producing draping simulations of a variety of woven fabrics. Our approach employs an interacting-particle model which is based on the microstructure of woven cloth, rather than utilizing a continuum approximation. Empirical data from a fabric testing device is used to tune energy functions within the model. We describe the model, how we convert the fabric test data to energy functions, and two experiments conducted to evaluate the approach. The first experiment produces non-linear mechanical data from the model. The second experiment compares photographs of three different types of draping cloth with visualizations of simulation results. The experiments show that we are able to reliably recover quantitative mechanical information from the model, and to reproduce the unique large-scale draping characteristics of a range of fabric types.