In this paper a new reduced formulation for modelling elastic structures or structural components with geometric non-linearities is presented. This formulation is obtained as a generalisation of the concept of foreshortening, which has been successfully used by other authors to model beams. Some examples are provided which illustrate the generality and validity of this formulation. The proposed theory is compared to previous work related to foreshortening, variable reduction in non-linear elastic problems and the use of a geometric stiffness matrix. Some guidelines are also given so as to implement the proposed method and to interpret the concepts that it involves. The reduction method presented is general, but a corrotational approach is followed to simplify the exposition.