A simplified theoretical model for the directional drilling tendency of a drill bit in anisotropic rocks is proposed. Deviational forces play a very important role in this model. To analyze the deviational forces a three-dimensional mathematical model of the static deformation of drill strings is presented. The effect of twisting torque on deviational force is studied with this model. The results show that the torque has very little effect on the deviational force in the plane of the gravitational force and a linear but negligible effect on the deviational force in the perpendicular plane. So the effect of torque is ignored and the analysis is reduced to two dimensions. A method is developed using singularly functions to represent the concentrated load in the simplified 2-D analysis of the drill string with stabilizers. Application of this method to the study of the effects of stabilizers and deviational forces produces satisfactory results. Further studies of the three-dimensional rock failure characteristics are needed to complete the theoretical model for directional drilling.