The objects of this paper are to study the effects which the eccentricity at a story causes on the dynamic characteristics of multi-story structure. Three kinds of eccentricity studied are the cases that shifts the center of rigidity only, the center of gravity only, and shifts both centers together. The ratio of eccentricity and the story with eccentricity are changed. The principal results of this study are as following; 1. There are few effects of the eccentricity on the natural periods of the structure, furthmore, the change of the translational displacements and the shearing stresses, caused at each story when subjected to earthquake ground motion, are little, too. 2. Regardless of the type of eccentricity, large torsional displacement and moment responses are caused at all stories. 3. At the structures shifted the center of rigidity, the torsional displacement and moment of the story with eccentricity grow larger, extremely. 4. These eccentricities which shifted the center of gravity at upper story and the center of rigidity at lower story, are caused some harmful results on the structure, particularly. 5. Some different properties are revealed between the results by statical analysis to the characteristics from dynamic response.