An analysis has been conducted to determine stresses and displacements near the center of long viscoelastic cylinders. Stresses arise due to thermal expansion and irradiation-induced dimensional changes which are anisotropic in transverse planes (i.e., planes perpendicular to the axis of geometrical symmetry). The explicit solution for stress is made possible by the assumption of a linear creep law. The logic is shown for a mathematical model that accounts for finite displacements. The model is used to predict stresses and displacements in borated-graphite absorbers used in the Peach Bottom high-temperature gas-cooled reactor (HTGR). It is predicted that fracture will not occur in the absorbers. This conclusion is presented with the reservation that there is considerable uncertainty regarding irradiation-induced dimensional changes due to the small amount of available data. However, the assumed values for these parameters are believed to be conservative.