Abstract The only standard drillstring model in use today is the torque-drag model, and because of the simplicity and general availability of this model, it has been used extensively for planning and in the field. Field experience indicates that this model generally gives good results for many wells, but sometimes performs poorly. In the standard torque-drag model, the drillstring shape is taken as the wellbore shape. Considering that surveys are taken within the drillstring, this is an excellent assumption. However, given that the most common method for determining the wellbore shape is the minimum curvature method, the wellbore shape is less than ideal, because the bending moment is not smooth at survey points. This defect is dealt with by neglecting bending moment, but as a result of this assumption some of the contact force will also be neglected. If the wellbore shape is the drillstring shape, why not use analytic drillstring solutions to model the wellbore trajectory? Before these solutions can properly interpolate the survey data, they require some modification. This paper shows how this can be done in a simple and efficient way, so that little of the calculation speed of the conventional model is lost. With this new wellbore model, the simple torque-drag model becomes a full stiff-string formulation. The paper gives a complete description of the wellbore trajectory calculation, including tests of circular, helical, and catenary trajectories to verify the accuracy of the formulation. Several example problems with different inclinations and wellbore curvatures are studied to compare the two torque-drag formulations. These studies give comparisons in execution time, drag forces, and torques for the two models, and for the new formulation, the magnitude of the bending moments.