The effect of magnetic fields on the shear stress of liquid crystalline polymers (LCPs) under shear flows is numerically analyzed using the Doi theory. The evolution equation for the probability density of LCP molecules is directly solved without any closure approximations. When the magnetic field is imposed on the LCPs along the shear flow, the low-shear rate plateau of the time-averaged generalized viscosity (eta) over bar*(= (sigma) over bar (xy)*/gamma*) disappears, which is due to the manner of the new aligning mode observed by Fu et al. The negative first normal stress difference NI becomes opposite in all the shear rate regimes with the disappearance of periodic oscillations. For the magnetic field parallel to the velocity gradient direction, the more complicated sign changes of (N) over bar (1)* is investigated because of the moment caused by the magnetic field vertical to the one caused by the shear flow. The ratio (N) over bar (2)*/(N) over bar (1)* increases with the increasing magnetic field strength. Finally, when the molecular shape parameter is considered as 0.9, the similar discussions are achieved according to the phase diagram among tumbling, wagging, and aligning modes versus the magnetic field strength. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1919-1926, 2010