Ongoing research into interlaminar stresses and delamination failure in laminated composites has pointed out the lack of a practical and reliable method for measuring the through-the-thickness strength of composite materials, a necessary parameter in any strength-of-materials approach for prediction of delamination initiation and growth. In this work, a specimen has been developed that allows 13.4-mm-thick laminates to be tested to failure in pure σzz (out-of-plane tension, or “flatwise loading”). This is achieved by bonding aluminum loading bars to a composite specimen tapered through its thickness. This specimen allows direct measurement of the through-the-thickness strength of such laminates. This specimen was used to measure both the transverse and through-the-thickness strength of AS4/3501-6 graphite/epoxy. The transverse strength of 57.6 MPa obtained showed good correlation with that measured with standard coupons, giving confidence in the specimen design. The measured through-the-thickness strength was 43.0 MPa. The through-the-thickness strength appeared to be independent of layup, as unidirectional and cross-ply laminates yielded only negligibly different results. Suggestions are also given as to how the specimen can be improved to facilitate manufacture and testing.