The greatest difficulty in modeling a nucleic acid is generating the coordinates of its furanoses. This difficulty arises from constraints imposed by the closed ring geometries of these sugars. We have developed a new method for modeling these furanose rings. Using this method, the coordinates of a sugar can be obtained quickly and unambiguously for any point on the pseudorotational pathway from one parameter: the phase angle of pseudorotation P. The significant difference between this and previous sugar modeling schemes is that here the endocyclic bond lengths of the five-membered sugar ring are allowed to vary a small amount according to simple, explicit, and experimentally reasonable analytic functions of P. The coefficients of these functions follow from the empirical behavior of the endocyclic bond angles and from geometrical constraints due to ring closure. The ability to model the sugars directly from one parameter greatly facilitates carrying out the global conformational studies on nucleic acid constituents which will be attempted in subsequent papers of this series.