The current specification provisions for the prediction of lateral restraint forces in Z-purlin supported roof systems under gravity loads are in Section D3.1 of the 1996 AISI Cold-Formed Specification. The design equations contained in these provisions are empirical and based on statistical analysis. They were developed using elastic stiffness models of flat roofs and were verified by experimental testing. The provisions need refinement, because the treatment of roof slope and system effects is incorrect. Also, the current design provisions are based upon an assumed panel stiffness value, ignoring the significant difference in required restraint force that occurs when panel stiffness is varied. Therefore, a new restraint force design procedure, having a stronger reliance on engineering principles, is proposed. This new treatment of the static forces in Z-purlin roofs led to a more accurate method of addressing roof slope. Elastic stiffness models, with varying roof slope, panel stiffness, and cross-sectional properties, were used to develop the proposed procedure. The basis of the procedure is to determine the lateral restraint force required for a single purlin system and then extend this result to systems with multiple restrained purlin lines. Roof slope is incorporated into the calculation of the single purlin restraint force, which includes eccentric gravity loads and forces induced by Z-purlin asymmetry. The procedure includes a system effect factor to account for the observed nonlinear increase in restraint force with the number of restrained purlins. An adjustment factor varies the predicted restraint force depending on the shear stiffness of the roof panel. The proposed procedure applies to five bracing configurations: support, third-point, midspan, quarter point, and third-point plus support restraints. / Master of Science