Nuclear reactor facilities often include segments of long tubular structures such as cooling water intake conduits, electrical ducts, and water well casings that are buried underground. During an earthquake such a buried structure responds to various seismic waves propagating through the surrounding soil as well as to the dynamic differential movements of the buildings to which the structure is connected. A rigorous analysis of the problem should consider the time-dependent stresses in the structure due to all the causes simultaneously. Such an analysis is beyond current technology at present. This paper presents a procedure to estimate the stresses due to various effects separately and then to combine them properly for design purposes. The resulting stresses can then be combined further with other applicable stresses to satisfy the design requirements. The analysis assumes that the soil is linearly elastic and homogeneous and the structure is a straight slender solid or hollow beam with a uniform, symmetrical cross section that satisfies the conditions of the elementary theory of slender beams.