This article aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that it is possible to adapt the immersion and invariance technique to design static state‐feedback controllers that solve this problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels.