Following the development of Mitchell, this report presents a mathematical study of 2-D Soft and Stiff String Torque Analysis with pipe rotation, and a 3-D Soft and Stiff String Drag Analysis with pipe running in and pulling out. The Torque Analysis has revealed some defects in the conventional formulation. Compared with conventional formulation, for pipe rotation, the term square root of (1 ?f^2) needs to be included in the contact force calculation. Comparing the torque calculation equations of 2D Soft and Stiff models, the calculated results are very close. The change in azimuth results in different doglegs of wellbore, which has great effect on axial force transfer.