Plane strain compression tests, measuring both axial and transverse forces, are performed on ultra-high molecular weight polyethylene Lip to true axial strains of -0.4. As the deformation proceeds, the transverse stress becomes an increasing proportion of the axial stress, with the proportion growing from its initial value of 0.5 up to a value of 0.8. A constitutive model is applied that combines Ogden models and Eyring processes. It is found that when a Levy-Mises flow rule is used in conjunction with the Eyring model, the predicted ratio of transverse to axial stress remains much smaller than that observed, and is not greatly affected by changes in the Ogden exponent. However, when the flow rule is replaced by one that incorporates strain-induced anisotropy, realistic predictions are possible. For each Ogden model, we associate a flow rule for which the transverse strains in both the Ogden and Eyring models are individually zero. (c) 2008 Wiley Periodicals, Inc. J Appl Polym Sci 111: 1.190-1198, 2009.