This thesis will consider two different theories, and apply variational techniquesto each, in order to investigate their true ground states and the possibility ofsymmetry breaking.A scalar field theory is modified by introducing a variational mass-parameter,which also serves as a regularization. The effective potential is calculated to twoloops, and a variational calculation is done to find the extrema of the potential.Secondly, the model of Wess and Zumino is modified by removing the re-strictions on the particle masses. The vacuum energy is then calculated to twoloops, and a variational calculation is performed with the renormalized massesas parameters, in order to determine the true ground state of the theory.It is discovered that the scalar field theory does not develop any symme-trybreaking groundstates, as was predicted by Coleman and Weinberg. Thenon-renormalization and vanishing vacuum energy of the Wess-Zumino model isverifed to two-loop order. Furthermore, it is discovered that the modified Wess-Zumino model has several groundstates which are more energetically favouredthan the supersymmetric state, in which supersymmetry is strongly broken.This may begin explain, if they exist, why we do not see any supersymmetricpartners in our accelerators.