This paper focuses on the typical regular R. C frame structure. Considering the fact thatframe structure still works at its elastic stage under frequent horizontal seismic action, and based on theprinciple of structure optimum design and the theory of anti - seismic design, a structure optimum modewhose control objective is apex lateral displacement is presental for frame structure.And an optimunobjective function is consequently determined . Finally this paper gives the calculation formula for sections'dimension of beams and columns of typical regular R. C frame structure. And the form of beamsnd columns optimum rigidity ratio is presented for engineers' reference.