Abstract The ASTM D3518/D3518M-94(2001) Standard Test Method for “in-plane shear response of polymer matrix composite materials by tensile test of a ±45° laminate” is based on the uni-axial tensile stress–strain response of a ±45° composite laminate which is symmetrically laminated about the midplane. For long glass fibre-reinforced epoxy composites, the test shows a highly nonlinear shear stress–strain curve. This work is concerned with the development of a material model to predict this mechanical behaviour. Part I discusses the experimental program with tensile tests on [+45°/−45°]2s laminates and off-axis [10°]8 composites. Cyclic tensile tests have been performed to assess the amount of permanent shear strain and the residual shear modulus. Part II focuses on the development of the material model and the finite element implementation. Two state variables have been introduced to represent the shear modulus degradation and the accumulation of permanent shear strain. The model has also been applied to the simulation of a three-point bending test on a [+45°/−45°]2s laminate.