[en] A hamiltonian variational procedure is discussed for lattice gauge theories, suitable for 3+1 dimensions, based on a trial state vector in terms of link variables. This method has been applied to the calculation of link and plaquette expactation values for the pure SU(3) lattice gauge theory. Agreement with Monte Carlo data is found only in part of the weak coupling cross over region. Taking some 2-link correlations in the trial state vector into account the results are improved in the cross over region and smear out an unwanted phase transition. (author)