Draping of woven fabrics and garments interacting with rigid objects or human bodies is a large displacement/rotation contact problem of anisotropic materials. The objective of this paper is to extend a geometrically nonlinear "nite-volume method recently developed by the authors to predict contact drape deformations of woven fabrics. In this "nite volume method, an initially #at woven fabric sheet is "rst divided into a number of structured "nite volumes (or control volumes) using mesh lines along the warp and weft directions. The out-of-plane bending and in-plane membrane strain energies of the fabric sheet are then found by summing up the contributions from all control volumes. The equilibrium equations of the fabric sheet are derived employing the principle of stationary total potential energy and solved using the full Newton}Raphson method with line searches. In this paper, a simple and easily achievable algorithm for detecting and treating fabric contact with a rigid object is proposed and shown to be e!ective and e$cient. Numerical simulation of two square fabric sheets draped over a round rod is "rst considered. The coordinates of a characteristic point of the "rst fabric sheet after drape deformation predicted using the present method are compared with available experimental results, showing a close match between the two approaches. Numerical results of square fabric sheets draped over a sphere and skirts attached to and draped over a synthetic body form are next presented. The predicted drape shapes are realistic.