This report describes Bureau of Mines research to develop methods to evaluate loading on longwall roof supports to permit better design and more efficient utilization of these structures in compliance with the geological conditions in which they are employed. The resultant vertical and horizontal force acting on the canopy of a shield can be determined, either from a statically determinate solution assuming rigid-body mechanics and elimination of certain unknowns, or from an elastic solution by analysis of the load- displacement relationship of the shield structure. A two- dimensional rigid-body model is presented that determines resultant shield forces by measurement of leg, canopy capsule, and lemniscate link forces. An elastic solution is presented in the form of an elastic stiffness model with two degrees of freedom, which describes the load-displacement relationship from the stiffness of the shield structure as determined in the Bureau's mine roof simulator (mrs). The ability of both models to determine resultant forces acting on the shield canopy are evaluated from full-scale tests in the mrs. More advanced numerical models are also discussed as part of the Bureau's continuing effort in the evaluation of roof support structures.