A new Mg alloy with a high number density of basal plate-shaped Guinier-Preston (GP) zones has been developed, within the Mg-Al-Ca-Mn quaternary system. Comprehensive reports of the mechanical properties and microstructure of these alloys have already been published, which reveal the strength and ductility to be similar to conventional Al extrusion alloys, such as AA6061. The alloy is obviously composed of low cost ingredients, and the ability to be extruded at speeds typical of Al alloys renders this alloy economically viable. The use of crystal plasticity modeling enables parsing of the strengthening contributions that grain size, substitutional solute, and GP zones make on each of the active dislocation slip and twinning modes. The hexagonal crystal structure permits, for the first time ever, measurement of the resistance that GP zones pose to the glide of dislocations both parallel and perpendicular to the zones. Beyond taking into account the geometry of the problem, it is revealed that GP zones offer little resistance to glide of basal dislocations, which shear the material on a plane parallel to GP zone (a monolayer enriched in solute atoms). However, they offer significant resistance to actual shearing of the zones by dislocations gliding on prismatic planes.