Unidirectional laminates have been tested under uniaxial transverse compression and under biaxialtransverse compression. Failure occurred by shear in an inclined failure plane parallel to the fibres.The transverse shear response of the material on the failure plane was evaluated from the tests. In thebiaxial tests, the failure load was considerably higher than in the uniaxial tests. For a given transverseshear strain the transverse shear stress was also higher in the case of biaxial compression. It is alsoshown that using waisted specimens instead of prismatic specimens does not seem to bring noticeablebenefits for through-thickness uniaxial compression tests. The experimental results presented here areimportant input to the development and the validation of damage models of fibre reinforced polymermaterials accounting for the matrix nonlinear response in shear and compression.