The ASME Section III design-by-analysis approach provides stress criteria for the design of nuclear components. Stresses are calculated elastically for the most part, although plastic analysis is recognized. Limits are specified for primary, secondary, and peak stresses. Inherent in these limits are factors of safety against several modes of failure. The purpose of this paper is to explain the design-by-analysis criteria and fundamental concepts behind the approach. Topics covered include the bases for the primary stress limits, shakedown to elastic action, fatigue, simplified elastic-plastic analysis, and thermal stress ratchet. Issues that are explored are separating primary and secondary stresses in finite element analyses, material ductility requirements, and the meaning of the fatigue penalty factor.