This paper deals with the development of a new formula for the critical moment (Mcr) of lateral torsional buckling of a beam for extreme conditions of its support for bending My (i.e. simply support or complete restraint) and simultaneous occurrence of elastic restraint against warping (κω) and against lateral rotation (κu) at the supports. For specific parameters (κω, κu) defining the boundary conditions of lateral torsional buckling of the beam, the full and mutually independent range of elastic restraint degrees was taken into account, from their complete freedom (κω = 0, κu = 0) to their complete fixity (κω = 1, κu = 1). Single-span beams with a hot-rolled bisymmetric I section (or its welded equivalent) were considered. The most common beam loading schemes encountered in engineering practice were taken into account. In constructing the new approximation formula, the concept of the integrated interaction coefficient was used according to the idea presented in the previous work of the authors. Small percentage differences of the estimated Mcr(κω, κu) values, compared to finite element method (LTBeamN), allow us to conclude that the proposed new formula gives sufficiently accurate results. The algorithm used in this paper to create approximation formulas may allow for taking into account a larger number of degrees of beam elastic restraint. The subject of further research will be the interactive consideration of three technically important conditions of elastic beam restraint, i.e. elastic restraint of warping, elastic restraint of lateral rotation (rotation in the lateral torsional buckling plane) and elastic restraint of rotation relative to the major axis of the cross-section (rotation in the bending plane).