Based on a graphical representation of intrachain contacts, we have developed a new three-dimensional model for the statistical mechanics of double-stranded chain molecules. The theory has been tested and validated for the cubic lattice chain conformations. The statistical mechanical model can be applied to the equilibrium folding thermodynamics of a large class of chain molecules, including protein beta -hairpin conformations and RNA secondary structures. The application of a previously developed two-dimensional model to RNA secondary structure folding thermodynamics generally overestimates the breadth of the melting curves [S-J. Chen and K. A. Dill, Proc. Natl. Acad. Sci. U.S.A. 97, 646 (2000)], suggesting an underestimation for the sharpness of the conformational transitions. In this work, we show that the new three-dimensional model gives much sharper melting curves than the two-dimensional model. We believe that the new three-dimensional model may give much improved predictions for the thermodynamic properties of RNA conformational changes than the previous two-dimensional model.