Data from several current tokamak experiments indicate that the equilibrium perpendicular velocity field can become strongly sheared accompanying the transition from the L mode to the H mode, i.e. improved, confinement, and that fluctuation levels are reduced. Linear theory suggests that velocity shear can stabilize ion‐temperature‐gradient (ITG) modes when the frequency shift experienced by the mode due to the radial dependence of the Doppler shift is comparable to the growth rate. To confirm the predictions of linear theory and to explore nonlinear issues, e.g., self‐generated shear flows, saturation amplitudes, and the concomitant energy transport levels, two‐ and three‐dimensional gyrokinetic simulations of ITG modes have been performed. The simulations were done with and without magnetic shear in a slab configuration using the partially linearized (&dgr;f) algorithm to reduce statistical noise. The simulations confirm theoretical analyses of the stabilizing and destabilizing effects of imposed perpendicular velocity fields. The ion energy transport levels at saturation follow the trends of the linear growth rates and the mixing‐length estimates. The gyrokinetic simulations are in qualitative agreement with the results of gyrofluid simulations, and exhibit saturation amplitudes and energy transport similar to those in gyrofluid simulations. These transport levels are generally lower than those typically reported in the laboratory experiments; including toroidal driving terms significantly increases the transport levels in the simulations.