Abstract: A nonlinear finite element method is proposed for geodesic line generation in cutting pattern for cable-enforced membrane structures. The minimum potential energy principle is used to prove that the balance of equal-tension geometrical nonlinear cables is achieved at the geodesic line when it slides freely on membrane surface. Two-force support rods normal to membrane surface on every node of cable are appended so that the cable can slides freely on membrane surface. The nonlinear finite element method is used to get the equilibrium location of the cable. The method is shown to exhibit good and rapid convergence.