The use of composite materials in structural applications ranging from aircraft and space structures to automotive and marine applications instead of conventional materials such as steel and Aluminum, has gained a growing interest. Although advanced composites exhibit desirable properties such as high specific stiffness and strength, temperature and chemical resistance, and relative easy processing, they have a number of limitations. One well known problem of fiber composite materials is their susceptibility to damage which may lead to structural failure under static and fatigue loads. The importance of the damage tolerance problem in composites is reflected in the volume of research publications devoted to this topic. Impact loads that can be applied to the composite structures may be axial, flexural or torsional impact. In this research, the residual flexural and torsional strength of glass-polyester U-beams and L-beams made by hand lay-up method has been investigated. Simulation of the problem has been done in the finite element software ABAQUS/Explicit and in order to investigate damage initiation, the four failure criteria of maximum stress, maximum strain, Hashin and Hou have been compared with each other in flexural impacts and the two failure criteria of maximum stress and maximum strain have been compared in torsional impacts. In addition to these failure criteria, instantaneous damage evolution law has been used. Experimental tests have been performed to validate simulations. By comparing the results of experiments and simulations it was concluded that for flexural impact of U beams, all four failure criteria have had acceptable predictions. But for L beams, Hou criteria have predicted much damage in the beam. Both maximum stress and maximum strain failure criteria have not had predicted the damage after torsional impact precisely. Because of a little inconformity between experiments and simulations. Keywords : Composite materials, Channel section beams, Hand lay-up, L-beams, Flexural impact, Torsional impact, FEM, Subroutine VUMAT