We extend the concept of best-fitting paraboloids for large single and dual reflectors with conic-section surfaces to best-fit shaped surface for large dual reflectors shaped for uniform amplitude distribution. The point focus of the paraboloidal main reflector is replaced by focal lines for the main reflector and the primary subreflector focus, whereas the secondary subreflector point focus at the feed is kept. The reflector surfaces are shaped, and all rays from the main-reflector aperture to the feed meet an equal-path-length condition. This condition may be represented by a set of "homology parameters" determined by a least-squares method. Finally, we calculate the homology parameters and the root mean square of surface errors for an 8-m dual-reflector system including gravity effects for the antenna pointed toward zenith and the horizon. 2017 IEEE.