Probabilistic methods have been developed that estimate the site-specific probabilities of the amino acids in sequences likely to fold to a particular target structure, and such information can be used to guide the de novo design of proteins and to probe sequence variability. An extension of these methods for the design of symmetric homo-oligomeric quaternary structures is presented. The theory is in excellent agreement with the results of studies on exactly solvable lattice models. Application to an atomically detailed representation of proteins verifies the utility of a symmetry assumption, which greatly simplifies and accelerates the calculations. The method may be applied to a wide variety of symmetric and periodic protein structures.