In many dynamic stress problems, the knowledge of the physical phenomena is not precise enough to justify exact predictions with respect to the results of each individual observation. On the one hand, the loading is never exactly known, and on the other, the physical system may be so complicated that detailed calculations for the prediction of dynamic responses are difficult and the numerical results are often uncertain. In such cases the physical data can be regarded as a set of statistical data of random processes. Logical statements of the forcing functions are therefore statistical. The chief object of an analysis is then to draw valid inferences about the statistical statements of the responses. In this paper the statistical theory is illustrated by the gustand landing-load problems. A method of determining the mean intensity of the dynamic response is presented. Through a study of the distribution of the extreme values, an "envelope" representing the most probable largest stress (or other response quantities of interest) at any point in the structure can be found. Such an envelope, if used as a basis for specifying the design stresses, can be regarded as one that yields, in the long run, a uniform factor of safety over the entire structure with respect to a random forcing function. The probability of exceeding a given maximum stress being known, the life expectancy of an aircraft can be determined as a function of the specified load intensity and vice versa.