Abstract Work on the axial compression of axisymmetric tubes, to be used in energy absorbing applications, has been extended to cones. This paper describes the results of compression tests on a range of truncated conical shells made from a chopped strand mat glass/polyester material. For cones with a wall thickness greater than 2 mm, failure occurs by progressive crushing which starts at the small end: unlike tubular specimens, no trigger is necessary. The specific energy absorption varies with cone angle, wall thickness and diameter in a complex way, and in some cases exceeds the values recorded for axisymmetric tubes. The crush zone morphology and failure micromechanisms also vary with specimen geometry. An initial assessment has been made of the relationship between energy absorption and failure mode.