Second-harmonic generation is described by the second-order nonlinear susceptibility χ(2) which, in the electric-dipole approximation, requires a noncentrosymmetric medium. It is very challenging and of high technological interest to search whether it is possible to find a way to break inversion symmetry in centrosymmetric crystals in order to induce second-order nonlinearities. A new intriguing way to observe second-order nonlinear phenomena is strain. Here, we present a detailed analysis of the correlation between the strain and the χ(2) in both centrosymmetric and noncentrosymmetric materials. We considered Si and SiC as test materials and we studied different types of strain (tensile/compressive), in different directions (uniaxial/biaxial) and for different light-polarization directions. We found which is the type of strain necessary in order to induce, tune, and enhance second-harmonic generation in different energy regions for centrosymmetric and noncentrosymmetric materials.