The molecular Doi theory of rigid rod polymer rheology is used to describe the experimentally observed electrorheological effect of liquid crystalline polymer solutions. Two‐dimensional Doi theory has been modified by including the electric potential energy of a dipole in the energy term of the diffusion equation and in the free energy expression. Based on the same model, a linear theory of viscoelasticity has been developed to predict the storage and loss moduli under the influence of an applied electric field. Calculations indicate that molecular orientation induces viscosity enhancement, while the model attributes nonzero storage and loss moduli to the distortion of the orientation distribution function. Molecular parameters in the model can be estimated from either theory or experiment. Using a constant rotational diffusivity, model predictions of low shear electroviscosity and low‐frequency storage and loss moduli agree well with experimental data for poly(n‐hexyl isocyanate) solutions.