We use a finite-difference algorithm to simulate the shear flow of nematic liquid crystals based on the Leslie-Ericksen theory, and investigate how unequal elastic constants affect the formation, oscillation, and breakup of roll cells, the nucleation of defects, and the coarsening of texture upon cessation of flow. With elastic anisotropy, the, so-called Ericksen number (Er) cascade comprises the same regimes previously documented for isotropic elasticity: stable simple shear, steady roll cells, oscillatory roll cells, and an irregular pattern with thick disclinations. The onset of roll cells is most sensitive to K-3, the elastic constant for bend. Increasing K-3 stabilizes the shear flow against the formation of rolls. For reduced K-3, a second Er cascade may appear for higher Er, with regularization and eventual reappearance of the defect-laden irregular pattern. The twist constant K-2 is the most important for defect formation; a weaker K-2 causes roll cells to breakup and pairs of +/-1 defects to nucleate at lower Er. The defects show distinctive structures depending on the elastic anisotropy; typically a weaker elastic constant gives rise to patterns that incur greater distortion in the corresponding mode. After cessation of shear, all textures relax completely to a monodomain. The longest-lasting orientational pattern is again attributable to the weakest of the elastic constants. By analyzing the amount of distortion in each mode and the associated free energy, we are able to elucidate the role of elastic anisotropy in defining the orientational patterns in sheared nematics. (C) 2003 The Society of Rheology.