An extrapolation method is presented for the evaluation of compression strength of unidirectional composites. We recommend that the thickness of the laminate tested range from 12 to 16 plies and that the gage length equal 5.08 mm. Three or more different tapered angles should be used for the end tabs. Each specimen geometry must have at least three replicates. Strain gages (or other instrumentations) must be placed on both sides of a specimen to ascertain that the strength value obtained is not due to premature failure. The strengths are correlated with the end tab tapered angles by a second-order polynomial function. The compressive strength can be extrapolated from this curve by setting the tapered angle of the end tabs equal to zero. At this state, the stress concentration vanishes theoretically. Our limited experimental results show that the compressive strengths of the Gr/Ep AS4/3501-6 and S-Gl/934 unidirectional laminates are -1885 and -1665 MPa, respectively. These values are significantly higher than those obtained using the Celanese or the classical IITRI specimens. Fiber failure was the major failure mode obtained from the specimens proposed here.