Efficient numerical methods for simulating cloth deformations have been identified as the key to the development of successful computer-Aided Design systems for clothing products. This paper presents the formulation of a new finite-volume method for the simulation of complex deformations of initially flat woven fabric sheets under self-weight or externally applied loading. The fabric sheet is assumed to undergo very large displacements and rotations but small strains during the process of deformation. The fabric material is assumed to be linear elastic and ortho-tropic. The fabric sheet is discretized into many small structured patches called finite volumes (or control volumes), each containing one grid node and several face nodes. The bending and membrane deformations of a typical volume can be defined using the global co-ordinates of its grid node and surrounding face nodes. The equilibrium equations governing the complex deformations are derived employing the principle of stationary total potential energy. These equations are solved using a single-step full Newton-Raphson method which is found to be capable of predicting the final deformed shape, the only result of interest in a fabric drape analysis. To speed up convergence, the line search technique is adopted with good effect. This single-step approach is more efficient than the step-by-step incremental approach employed in conventional non-linear finite element analysis of load-bearing structures. A number of example simulations of fabric drape/buckling deformations are included in the paper, which demonstrate the efficiency and validity of the proposed method.