In an effort to gain a fundamental understanding of the electromechanical response in high mobility crystalline organic semiconductors, we have investigated the uniaxial strain-mobility relationships in rubrene and benzothienobenzothiophene crystals. Elastic moduli and Poisson ratios of the materials are evaluated and the strain mobility response of these materials is rationalized using the effective masses and electronic couplings in the framework of hopping and band transport models, giving consistent results. The microscopic origin of the response is investigated in relation to the strain induced variations in the inter- and intra-molecular degrees of freedom. We demonstrate that the strain applied along one of the crystallographic directions in these materials does not only induce mobility variations along the same direction, but also along the other crystallographic directions that are mechanically coupled with large Poisson ratios. A rational design of electronic devices could therefore benefit from the efficient exploitation of this anisotropic strain mobility response in relation to the inherent crystalline anisotropy.