Seismic anisotropy in the upper mantle is due primarily to preferred orientation of olivine crystals induced by progressive deformation. In order to understand better the origin of seismic anisotropy, we present a simple theory for plastic deformation and textural evolution of olivine polycrystals. Each crystal in the aggregate is assumed to deform by intracrystalline slip on three major slip systems, whose hardnesses and stress exponents are known from experiments. The evolving grain orientation distribution in the aggregate is calculated by minimizing the difference between the local (crystal) deformation and the global (aggregate) deformation subject to the constraint of global strain compatibility. The axial compression texture predicted by our model agrees well to first order with that determined experimentally by Nicolas et al. (1973), although there are significant discrepancies in the details. Our results suggest that the orientation texture developed during progressive plane strain deformation is a nearly unique function of the finite strain, such that the crystallographic axes <100>, <010>, and <001> are concentrated around the finite strain axes a, c, and b, respectively (a>b>c). This result may allow the state of finite strain at depth to be estimated from observations of seismic anisotropy. ¿American Geophysical Union