The gaussian variational approach is applied to pure Y-M theory in the axial gauge. Here restriction is made to the class of trial (vacuum) wave functionals that are invariant under space translations, rotations and color transformations. The resulting integral equation (gap equation) contains only renormalizable logarithmic divergences. The unique solution is found for any value of the coupling constant. The elementary excitation energy ω(k) behaves as k-0.77 for k → 0 and as k ln - 1 2(k/μ) for k → ∞. There exists a finite energy gap between the ground state and the lowest excited state.