In this paper the effects of saliency and cross-coupling in a cylindrical wound-rotor synchronous motor are evaluated within the operating region of the direct-axis, quadrature-axis and field excitations. In the calculation of the wound-rotor synchronous motor parameters, a finite element based approach (principle of frozen permeability) is followed to evaluate the inductances and flux linkages of the motor while incorporating the effect of saliency and cross-coupling. The classical two-axis machine model is adapted in order to take the effects of saliency and cross-coupling on the direct- and quadrature-axis inductances and flux linkages into account. The calculated inductances and flux linkages of the adapted two-axis machine model using the frozen permeability method show a great effect of saliency and cross-coupling. The contribution of saliency inductance and mutual cross-coupling inductance to the torque of the wound-rotor synchronous motor is also investigated using the frozen permeability approach. It is shown that the mutual cross-coupling torque component is severe in the wound-rotor synchronous motor, which can increase or reduce the resultant torque of the motor depending on the direct and quadrature axis load-current condition.