Organic semiconductors are intensively studied as promising materials for the realisation of low-cost flexible electronic devices. The flexibility requirement implies either performance stability towards deformation, or conversely, detectable response to the deformation itself. The knowledge of the electromechanical response of organic semiconductors to external stresses is therefore not only interesting from a fundamental point of view, but also necessary for the development of real world applications. To this end, in this work we predict and measure the variation of charge carrier mobility in rubrene single crystals as a function of mechanical strain, applied selectively along the crystal axes. We find that strain induces simultaneous mobility changes along all three axes, and that in some cases the response is higher along directions orthogonal to the mechanical deformation. These variations cannot be explained by the modulation of intermolecular distances, but only by a more complex molecular reorganisation, which is particularly enhanced, in terms of response, by π-stacking and herringbone stacking. This microscopic knowledge of the relation between structural and mobility variations is essential for the interpretation of electromechanical measurements for crystalline organic semiconductors, and for the rational design of electronic devices.