Germanium nitride, having cubic spinel structure, γ-Ge ₃ N ₄ , is a wide band-gap semiconductor with a large exciton binding energy that exhibits high hardness, elastic moduli and elevated thermal stability up to approximately 700°C. Experimental data on its bulk and shear moduli ( B ₀ and G ₀ , respectively) are strongly limited, inconsistent and, thus, require verification. Moreover, earlier first-principles density functional calculations provided significantly scattering B ₀ values but consistently predicted G ₀ much higher than the so far available experimental value. Here, we examined the elasticity of polycrystalline γ-Ge ₃ N ₄ , densified applying high pressures and temperatures, using the techniques of laser ultrasonics (LU) and Brillouin light scattering (BLS) and compared with our extended first-principles calculations. From the LU measurements, we obtained its longitudinal- and Rayleigh wave sound velocities and, taking into account the sample porosity, derived B ₀ = 322(44) GPa and G ₀ = 188(7) GPa for the dense polycrystalline γ-Ge ₃ N ₄ . While our calculations underestimated B ₀ by approximately 17%, most of the predicted G ₀ matched well with our experimental value. Combining the LU- and BLS data and taking into account the elastic anisotropy, we determined the refractive index of γ-Ge ₃ N ₄ in the visible range of light to be n = 2.4, similarly high as that of diamond or GaN, and matching our calculated value. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.