An analysis of the statistical mechanics of a densely cross-linked system is presented. It is argued that for such systems fluctuations of the cross-link points will be severely inhibited and the assumption of affine deformation should be reasonable. It is first demonstrated that the usual result obtained by classical theories can be obtained by an alternative method without assuming Gaussian statistics or the Langevin approximation for the partition function, For values of N, the number of "statistical segments" (freely hinged and rotating) between cross-link points, less than or equal to 2, the Gaussian results cannot apply. For small deformations of networks with N greater than or equal to 3, the Gaussian approximation is shown to be valid. This latter result will be employed in studies of the deformation of swollen coal gels in future work.