A calculation is made of the parity-forbidden two-photon absorption cross section of the transition between the lowest Stark sublevels for a tetragonal site Cc3+ (symmetry Ca,) in a cubic fluorite crystal as well a8 of polarizat.ion characteristics of a CaF, : Ce3+ monocrystal with different orientations ( k l ) LlOO], k 11 [llO], k 11 [ l l l ] , k is t.he wave vector of the incident laser beam). The calculated cross-sectional value (a, = 3.7 x m~-~ s) and the polarization dcpendences agree with experiment.