This short paper deals with an analogy between the deformation gradient in three-dimensional continuum mechanics and a generalized shell shifter tensor being employed in volume shell formulations. This analogy is very well suited to derive relations between the line, area and volume elements in the shell continuum and those located at the reference surface of the shell. Furthermore, strain and stress tensors can be derived in a very elegant way. Finally, the three-dimensional and two-dimensional strain-energy density is obtained in a very clear manner. The analogy found therefore gives a new and very powerful interpretation of the shell shifter tensor.