Using the nematodynamic equations of Ericksen and Leslie, we investigate the nature of the Freedericksz transition for elastically anisotropic nematic liquid crystals between parallel plates and subject to a shear and an external magnetic field. Two types of velocity profiles are considered: the simplified (linear) profile where the velocity gradient in the bulk of the sample is constant and a more realistic non-linear profile. We investigate and characterize the differences in the director distortions and the onset of transition in these cases for a range of external field strengths.