A modeling scheme that combines a constrained backbone generating algorithm with simple hard-sphere packing calculations is offered to build the four-stranded structures of DNA found in Holliday junctions. Two standard B-DNA duplexes are oriented side by side with helix axes at different relative inclinations and then systematically rotated and translated to identify closely spaced contact-free states. Attempts are subsequently made to introduce a low-energy sugar-phosphate linkage that serves as the site of strand exchange between the two duplexes. The chemical connection is sought using an algorithm which identifies the possible arrangements of the intervening backbone torsions between arbitrarily positioned bases. The goal is to identify the multiple conformational solutions associated with a particular arrangement of neighboring DNA helices in the four-way junction rather than a single optimum structure. The methodology is general, in terms of accommodating four-way junctions with arms of variable conformation and chain length and of dimensions much greater than treated heretofore. The only deformation in the four-way structures relative to B-DNA occurs at the site of backbone exchange, with base stacking and Watson-Crick pairing completely preserved in all models. The arrangements of neighboring bases at these sites resemble the unusual conformational steps found in a number of small molecule nucleic acid crystal structures. An interesting outcome of the calculations is the formation of sterically acceptable four-arm Holliday junctions over a wide range of angles at the cross. The potential mobility of the Holliday junctions is inferred from visualization and energetic analysis of the various models. Long-range electrostatic energies based on different currently available treatments of the dielectric constant are used to estimate the conformational preferences and flexibility of the four-stranded structures. The various dielectric schemes, however, are not in complete agreement on the likely conformational variability of the four-way junctions. The structures suggest a possible mechanism for branch migration and detail a pathway linking the antiparallel uncrossed Holliday structure inferred from solution measurements and the parallel cross-packed helical arrangements observed in single-crystal X-ray studies.