Up to now there have not been found suitable analytical solutions for P Cyg type line profiles. We have found an analytical solution for completely saturated singlet resonance lines of spherically-symmetric stellar wind using the Sobolev approximation. The limb darkening of stellar disk has been ignored and a special case of velocity law has been assumed. In this approximation the thermal structure of stellar wind has no influence on the line profile.

The formulae which enable to follow derivation of the profile function will be given. The line profile is expressed in elementary functions for duly formulated dimensionless ratios. The computed profile will be given in a figure. The profile can be considered as a standard for saturated spectral lines.

The result shows that the Sobolev approximation can be used without mathematical complications also for the subsonic wind velocities and in the region of terminal velocity. We hope that analytical solutions can be found also for description of wider set of observed spectral line profiles.