We have considered the problem of monochromatic radiation propagation through a uniaxial homogeneous medium. Two versions are shown for investigating the above-mentioned problem. The scalar approximation (no variations of the polarization state of radiation at propagation are taken into account) and the rigorous approach based on the exact solution of the vector wave equation. The basis for the first version is the suggested general determination of ordinary and extraordinary radiation, while in solving the wave equation we used the Kirchhoff-Helmholtz method generalized to vector problems. In both of these versions, simplification of solutions was considered based on the parabolic approximation. It is shown that in this case the results obtained using the scalar and vector versions for less divergent laser beams will, as assumed, coincide more closely.