Out-of-plane compression tests were conducted on six grades of ultra high molecular weight polyethylene fibre composites (Dyneema®) with varying grades of fibre and matrix, ply thickness, and ply stacking sequence. The composites with a [0°/90°] lay-up had an out-of-plane compressive strength that was dictated by in-plane tensile fibre fracture. By contrast, the out-of-plane compressive strength of the uni-directional composites was significantly lower and was not associated with fibre fracture. The peak strength of the [0°/90°] composites increased with increasing in-plane specimen dimensions and was dependent on the matrix and fibre strength as well as on the ply thickness. A combination of micro X-ray tomography and local pressure measurements revealed the existence of a shear-lag zone at the periphery of the specimens. Finite element (FE) and analytical micromechanical models predict the compressive composite response and reveal that the out-of-plane compression generates tensile stresses along the fibres due to shear-lag loading between the alternating 0° and 90° plies. Moreover, the compressive strength data suggests that the shear strength of Dyneema® is pressure sensitive, and this pressure sensitivity is quantified by comparing predictions with experimental measurements of the out-of-plane compressive strength. Both the FE and analytical models accurately predict the sensitivity of the compressive response of Dyneema® to material and geometric parameters: matrix strength, fibre strength and ply thickness. © 2014 Elsevier Ltd.