The objective of this study was to develop design equations that predict lateral restraint forces in two commonly used Z-purlin supported roof systems. These are quarter point bracing and third point plus support bracing. To that end, a stiffness model used in the past has been reintroduced. This model has been modified slightly to better represent roof system behavior. The updated stiffness model was then used to estimate lateral restraint forces for a number of roof systems with a varying cross sectional dimensions of the purlin, number of purlin lines, number of spans, and span length. A regression analysis was then performed on the data to obtain empirical design equations similar to those found in the 1996 Edition of the American Iron and Steel Institute's Specification for the Design of Cold-Formed Steel Members, Section D.3.2.1. <i>Vita removed April 4, 2011. GMc</i> / Master of Science