The linear optical response of lithium niobate under compressive as well as tensile stress is calculated from first principles. For this purpose, the elastic constants are computed with different exchange‐correlation functionals and compared with available experimental values. A good agreement with the measured quantities is obtained. A full set of the piezo‐optic and photoelastic coefficients is determined from the dependence of the dielectric permeability in the linear regime on the considered stress. The calculated coefficients agree with the experimental values as well. In contrast to the numerous experimental investigations, the coefficients are not only given for a single excitation wavelength but also within the technically relevant optical range. From the dispersion of the piezo‐optic and photoelastic coefficients, conclusions can be drawn about the refractive indices and the birefringence under strain for different excitation energies. It can be concluded that the birefringence in the long wavelength range increases under stress in the z direction. For uniaxial stress in x and y directions, the lattice symmetry is broken and the crystal becomes biaxial in the x and y directions as well.