Most investigations of large amplitude oscillatory shear (LAOS) rheometry to date have presumed uniform shear. The study of structured materials would especially benefit from LAOS rheometry but require the use of the larger gaps and roughened surfaces in parallel-plate and cylindrical-Couette geometries. However, in these geometries, the shear profiles are not homogeneous throughout the deformation field. For elastoviscoplastic materials undergoing LAOS in these geometries, both elastic and viscoplastic deformations may occur simultaneously, complicating the data analysis. By means of model simulations, we provide a comprehensive picture of a model elastoviscoplastic material undergoing oscillatory shear deformation in the parallel-plate and cylindrical-Couette geometries, and we compare the oscillatory signals to those obtained from a uniform-shear field. Both displacement-controlled and torque-controlled oscillatory flows were simulated. We show that using popular linear formulas for mapping displacement to strain and torque to stress results in strain and stress signals that deviate significantly from their uniform-shear counterparts. For some limited cases, specifically displacement-controlled parallel-plate and torque-controlled cylindrical-Couette oscillatory rheometry, the use of advanced mapping methods to improve the calculation of strain and stress signals was demonstrated. As an alternative, we suggest that analyzing LAOS signals via constitutive modeling provides a unifying approach. (C) 2013 The Society of Rheology.