Computerized molecular model building has been used to deduce the arrangement of sickle cell hemoglobin molecules (Hb-S) in the tubular fibers which form within sickling cells and in concentrated cell-free solutions of deoxygenated Hb-S. A "best" solution has been found which satisfies all of the reported properties of these fibers. In the proposed arrangement the contact between adjacent Hb-S molecules in the direction parallel to the fiber axis is primarily hydrophobic and in addition contains two salt bridges between the molecules. This contact would be disrupted with the Glu of Hb-A at the beta6 position instead of the Val of Hb-S, and it would not make a long fiber with oxygenated Hb-S. Residues in the A helix and the GH corner of the beta2 chain of one molecule are in contact with residues of the A, B, and E helices and the GH corner of the alpha1 chain of its neighbor. The intermolecular contact in the direction perpendicular to the fiber axis is mainly between the end of the E helix and the EF corner of the beta1 chain on the first molecule and the F helix and FG corner of the alpha2 chain of its neighbor. Some of the implications of these contacts are reported here, and others will be presented in subsequent papers.