Abstract: Based on anisotropic elastic theory,the linear and nonlinear constitutive equations of twistless fiber bundles were worked out by utilizing elastic mechanics.The curve of elongation properties of the fiber bundles was plotted according to the experiments of longitudinal extension and transverse compression of the bundles.The geometric relevance to deformation of the twisted fiber bundle was analyzed and the influence of twisting on performance parameters of the bundle was revealed by energy method.The importance of research of constitutive equation in projecting the mechanical behavior of textile composites materials was expounded.