Strain engineering has been used to increase the charge carrier mobility of complementary metal-oxide-semiconductor transistors as well as to boost and tune the performance of optoelectronic devices, enabling wavelength tuning, polarization selectivity and suppression of temperature drifts. Semiconducting nanowires benefit from enhanced mechanical properties, such as increased yield strength, that turn out to be beneficial to amplify strain effects. Here we use photoluminescence (PL) to study the effect of uniaxial stress on the electronic properties of GaAs/Al0.3Ga0.7As/GaAs core/shell nanowires. Both compressive and tensile mechanical stress were applied continuously and reversibly to the nanowire, resulting in a remarkable decrease of the bandgap of up to 296 meV at 3.5% of strain. Raman spectra were measured and analyzed to determine the axial strain in the nanowire and the Poisson ratio in the <111> direction. In both PL and Raman spectra, we observe fingerprints of symmetry breaking due to anisotropic deformation of the nanowire. The shifts observed in the PL and Raman spectra are well described by bulk deformation potentials for band structure and phonon energies. The fact that exceptionally high elastic strain can be applied to semiconducting nanowires makes them ideally suited for novel device applications that require a tuning of the band structure over a broad range.