Abstract: In order to describe the geometric characteristics of the centerline of borehole with directional survey data and predict the drag of casing in running, the relations among the unit base vectors in natural curvilinear coordinates and the deviation and azimuth angles along the borehole centerline are established. Then the total flexural curvature and the natural tortuosity of the centerline can be expressed with the change rates of deviation and azimuth angles. Some technical treatments are put forward to smoothen and interpolate the directional survey data along the centerline. On the other hand, the equilibrium state of a free-isolated stiff casing element is examined. The governing differential equations of the casing in running are formulated and solved using finite difference method. The constrained reactions and drag along the casing are obtained.