We employ an eigenpolarization model including the description of direction dependent excitonic effects for rendering critical point structures within the dielectric function tensor of monoclinic β− Ga 2 O 3 yielding a comprehensive analysis of generalized ellipsometry data obtained from 0.75–9 eV. The eigenpolarization model permits complete description of the dielectric response. We obtain, for single-electron and excitonic band-to-band transitions, anisotropic critical point model parameters including their polarization vectors within the monoclinic lattice. We compare our experimental analysis with results from density functional theory calculations performed using the Gaussian-attenuation-Perdew-Burke-Ernzerhof hybrid density functional. We present and discuss the order of the fundamental direct band-to-band transitions and their polarization selection rules, the electron and hole effective mass parameters for the three lowest band-to-band transitions, and their excitonic contributions. We find that the effective masses for holes are highly anisotropic and correlate with the selection rules for the fundamental band-to-band transitions. The observed transitions are polarized close to the direction of the lowest hole effective mass for the valence band participating in the transition.