A method of frequency domain analysis of secondary systems is extended, and an optimization method is presented for arch-type trusses under constraints on seismic response strains. The arch and the supporting structures are regarded as secondary and primary structures, respectively, and only the arch is to be optimized. In the proposed method, eigenvalue analysis of the primary structure is to be carried out only once at the beginning of optimization. Different damping characteristics between the two parts can be easily incorporated. The accuracy and computational efficiency of the proposed method are discussed in the examples.