In the horizontal well of long and middle radius, the drillstring of several thousand meters is in random contact with the bore hole wall in a large area along the well depth, which is a nonlinear contact problem. It is solved by the gap element method[1] in this paper so that the contact state is accurately described and the contact frictional resistance of drillstring is calculated. A great number of calculation examples for engineering have shown that the gap element method may correctly describe the con...