Theme T paper presents a technique developed for the analysis of stress concentration in axisymmetric viscoelastic solids with a moving inner boundary. Using White's procedure of viscoelastic analysis, the technique is then used to analyze a case-bonded grain, in which a number of axisymmetric slots are spaced at intervals along the longitudinal directions. Since the grain material constants are highly temperature sensitive, a general thermoviscoelastic analysis is formulated. However, the combination of low thermal conductivity coefficients and the burning rates typical of solid propellants leads to the assumption that the high flame temperature at a burning surface does not change the bulk temperature distribution in the propellant.