Abstract: Constructing the double layer multi-directional contactgap element to describe the random contact problem about slim tubing stringwith inside and outside string, combining with dimensional beam element andadopting variable and equivalent stiffness to solve equations, the contactcondition, the contact position, the size of friction and the generalizedinner force, stress and deformation in arbitrary well depth of the rod andtubing string were obtained. The arithmetic example about three wellsdemonstrated that the corrigendum of hang weight in well head was low by 10percent. Therefor, it supplied reliable computational methods andtheoretical references for designing and failure analysis of the rod andtubing string.