In this paper, inspired by Lagrangian mechanics, a marine craft is regarded as a mechanical system subject to both holonomic and nonholonomic constraints. Then, the forces that secure fulfilment of the constraints are derived. The proposed method is used to design a controller which makes the craft converge to straight-line paths with an exponential rate. A method to handle underactuation in sway is also proposed. Simulation results demonstrate the performance of the proposed method, and enlighten the effect of the new selection of constraints for the path-following problem.