A sheared slab magnetic field modelB=B0[zˆ+(x/Ls)yˆ], with inhomogeneous flows in theyˆandzˆdirections, is used to perform a fully kinetic stability analysis of the ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes. The concomitant quasilinear stress components that couple to the local perpendicular (ycomponent) and parallel (zcomponent) momentum transport are also calculated and the anomalous perpendicular and parallel viscous stresses obtained. A breakdown of the ITG‐induced viscous stresses are generally observed at moderate values of the sheared perpendicular flow. Even in the absence of external momentum sources, ion diamagnetic effects can generate an inhomogeneous radial electric field which gives rise to a sheared perpendicular flow which can sustain a sheared parallel flow. The effect of the perpendicular stress component in the momentum balance equations is generally small while the parallel stress component, which is primarily determined by the perpendicular flow shear, can dominate the usual neoclassical viscous stress terms. The large anomalous effect suggests that the neoclassical explanation of poloidal flows in tokamaks may be incorrect. The present results are in general agreement with existing experimental observations on momentum transport in tokamaks.