Several construction methods have been introduced to build the elements of BIBDs’ for specific parameters, with different techniques suggested for testing their existence, still no general technique to determine the efficiencies of these designs has been realized. In this study the efficiencies and relative efficiencies of Sum constructed automorphic symmetric balanced incomplete block designs with respect to parent designs has been presented. The process involved the classical analysis of variance applied to a data set. Computed relative efficiency of the design λ3 with respect to parent design λ1 has been found to be 1.216.