Polypropylene has been oriented by solid-phase deformation processing to draw ratios up to similar to 16, increasing tensile stiffness along the draw direction by factors up to 12. Nanoindentation of these materials showed that moduli obtained for indenter tip motion along the drawing direction (3) into to 1-2 plane (axial indentation) were up to 60% higher than for indenter tip motion along the 2 direction into the 1-3 plane (transverse indentation). In static tests, tensile and compressive determinations of elastic modulus gave results differing by factors up to similar to 5 for strain along the draw direction. A material model incorporating both orthotropic elasticity and tension/compression asymmetry was developed for use with Finite Element simulations. Elastic constants for the oriented polypropylene were obtained by combining static testing and published ultrasonic data, and used as input for nanoindentation simulations that were quantitatively successful. The significance of the tension/compression asymmetry was demonstrated by comparing these predictions with those obtained using tensile data only, which gave predictions of indentation modulus higher by up to 70%.