||The objective of the present study is to demonstrate a physically based method for cloth draping simulation of various fabrics. Based on continuum mechanics, the cloth deformations are described in Green's functional expression of energy. The fabric material constitutive relationship is built using anisotropic elasticity theory and fully account for in the animation. During draping, the fabric undergoes large rotation but small tensile deformation. The discretization of the cloth, which is meshed in the form of either rectangular or triangular network, is discussed. The corresponding motion equations are derived using finite difference and finite element methods respectively. The measured material parameters, such as tensile, shear and bending modulus, are incorporated into the dynamic equations, which govern the draped shape of the cloth. The constitutive evaluations of material behaviors for animation-based models are extended and developed. The constraint-based numerical solution scheme is proposed to avoid the cloth/body and cloth/cloth collision problems arising from the draping action. Simulations and applications in three dimensional garment design are presented. Results of the material-based draping simulation are shown to be realistically simulating the cloth-draping phenomenon.