A rational basis for the design of earthquake-resistant structures is developed. Structures designed on this basis will have uniform strength in the sense that each element will have an equal probability of successfully withstanding strong-motion earthquakes of the general type recorded by the Coast and Geodetic Survey, United States Department of Commerce, on the North. American continent. The theory is based on inferences drawn from accelerograms of strong-motion earthquakes and on the theory of probability. Although the general method of approach is capable of wider extension, the conclusions of the present study are limited to elastic structures founded on ground having a stiffness comparable to that of the sites at which reliable earthquake accelerograms have been recorded.