An understanding of the fundamental mechanism behind the relief of shear stress in single-crystal silicon subject to loading by shock-waves has to this day remained elusive. What is known is that this material undergoes a first-order pressure-induced polymorphic phase transition from its ambient pressure cubic-diamond (cd) crystal structure to its first stable high-pressure phase, known as β-Sn, at a pressure of about 120 kbar under hydrostatic compression. By investigating the evolution of the transition parameters for this phase transition as a function of increasing uniaxial shear stress representative of the effects of shock-compression via ab-initio Density Functional Theory computational techniques, we predict a significant lowering of the stress at which the phase transition occurs. This raises the question as to whether the onset of plastic response at the material's Hugoniot Elastic Limit (HEL) reported in experiments corresponds in fact to the phase transition itself, a very plausible possibility which has never been considered before. Furthermore, we present molecular dynamics simulations using a Tersoff-like potential of shock-compressed single crystals of silicon. We find an elastic response up to a critical stress, above which the shear stress is relieved by an inelastic response associated with a partial transformation to a new high-pressure phase, where both the new phase (Imma) and the original cubic diamond phase are under close to hydrostatic conditions. We note that these simulations are also consistent with shear stress relief provided directly by the shock-induced phase transition itself, without an intermediate state of plastic deformation of the cubic diamond phase.