The compression behaviour of unidirectional carbon fibre/epoxy composites has been widely investigated. The poor compression properties of the material relate to the material instability which leads to the formation of fibre kinkbands. At high fibre volume fractions, this instability results from the polymer matrix which is sheared due to the misalignment of the compressed fibres, culminating in yielding or fracture of the matrix or failure at the matrix-fibre interface. In this study, the shear response of an epoxy polymer matrix under pure shear and shear-compression deformation was investigated. Hollow, thin-walled Prime 27 epoxy specimens were manufactured by machining from cured epoxy cylinders. Experimental results showed that the specimens exhibited a uniform in-plane shear strain in the gauge section in both test modes. The average yield stress of the compression-shear specimens (51.0 MPa) was slightly lower than that of the pure-shear specimens (54.9 MPa), due to the applied compression stress. The shear moduli of the specimens for both test modes were consistent with only 3.8% difference. The applied compression stress delayed the specimen failure and achieved a higher fracture strain. The data collected in these tests will be used in finite element (FE) modelling to explore how the compression behaviour of unidirectional composites can be improved.