Composites are being widely used because of their high strength and stiffness, low density and high formability for creating complex shapes. An all-composite joint is a structural connector known for its ability to reduce the weight and assembly cost while retaining a good load-carrying capability. Based on the material characteristics of unidirectional fiber composites used in composite joints, a modified maximum stress failure criterion, which is able to assess damage onset, propagation and final failure, is presented for unidirectional fiber composites. The stiffness and strength of four types of composite joints under tensile and bending loads are simulated by progressive damage models, involving a finite element analysis, failure criteria and a material degradation model. Numerical results from the application of this criterion in nonlinear element analysis show good agreement with experimental outcomes.