The theory of screws can be seen as a central tool for modeling the kinematics and dynamics of spatial mechanisms, in particular robotic systems. Since screw theory is based on the assumption of perfect rigid bodies, it is not readily applicable to the analysis of flexible systems. This paper intends to contribute to an integral view of ‘displacements of rigid bodies’ and ‘deformations of flexible bodies’ by considering the geometry of linear spatial deformations in analogy to the geometry of linear spatial displacements. For this purpose, the principle of transference is applied to the system of double numbers. Thus, a dual-number based formalism for modeling linear deformations of flexible bodies is proposed including sibling versions of the Mozzi-Chasles theorem and the Euler-Rodrigues formula.