High density polyethylene with a single crystal texture has been used to examine the variation of yield stress with orientation in both tension and compression. The Coulomb yield criterion, which has previously been applied to yield data in oriented polyethylene, must be rejected since the experimental data can only be fitted over a limited range of orientation in tension only. A three-part criterion previously applied to fiber-composites gives a good fit to the tensile data; this model also predicts the changeover from ductile to brittle behavior observed in tensile specimens with theta greater than 70 degree ( theta is the angle between the tensile axis and the molecular axis). None of the yield criteria examined able to explain satisfactorily the lack of any marked degree of anisotropy in compression.