A procedure for finding complete numerical solutions for the elastic boundary layer field in wedges of a laminated composite strip under the generic loadings of generalized plane deformation is discussed together with numerical examples for free edge problems and delamination crack problems. The procedure yields the solution in terms of loading parameters and is applicable to an arbitrary wedge angle and ply orientation and any type of loadings within the range of generalized plane deformation. For the free edge problem, the so called free edge stress intensity and the mode vector are defined and the free edge stress intensity is found to be a single parameter governing the fracture or failure behaviour near the free edge for a given pair of adjacent materials (plies). The effect of relative ply thickness upon the stress intensity and the energy release rate is also discussed for various types of loadings.