In practice, the elastic lateral-torsional buckling of doubly symmetric I-section steel members is analyzed assuming free warping at supports. However, welded stiffeners, bolted end-plate connections or column base plates maintain elastically the opposite flange out-of-plane rotations and thus induce substantial warping restraints. This paper proposes analytical formulations for the evaluation of the elastic critical bending moment for lateral-torsional buckling of beams taking into account warping restraints at supports. Assuming series of displacement and rotation fields containing one or two terms, the energy method permits to derive expressions of the critical bending moment under constant and linear distribution of the bending moment. A single expression of the warping coefficient kw is proposed whatever the shape of the bending moment diagram. The factor C1 can be conveniently calculated by multiplying two coefficients that depend on the shape of the bending moment diagram and on the warping restraint stiffness, respectively. Finite Elements analyses of beams with warping restraints at supports have been performed considering a beam element model developed with LTBeamN and a shell element model created in ANSYS. The analytical model is in good agreement with the numerical results obtained by the two finite element models.