The transfer matrix method, developed earlier for the 2D square lattice has been generalized to enumerate and generate self-avoiding walks (chains with two ends) and self-avoiding circuits (no ends) in 3D on the cubic lattice. The method has been applied to Hamiltonian paths and circuits within simple geometries, i.e., parallelepipeds of size l x m x n for varying integer numbers l, m, n. The generalization of the method to irregular shapes has also been discussed, We also discussed an extension of this new method to permit random sampling of the conformational space.