A long pipe rests on the ocean bottom and it is gradually subjected to hydrodynamic forces due to water currents. Furthermore the motion of the pipe is resisted by soil reactions. The mathematical model for the plane deformation, consists of a nonlinear system of four ordinary differential equations, with four unknowns. To the system the appropriate boundary conditions at the two ends were added. The solution to the problem is connected to that of single nonlinear integral equation, which does not admit a closed solution. A closed solution is derived for the special case when the free end of the pipe is pulled through a given point. The solution is given in this case in terms of elliptic integrals of the first and second kind. (Author)