There is often a wide divergence of interest between the missile engineer responsible for thrust performance on the one hand, and the motor tube manufacturer concerned with chemical composition on the other. The propellant grain design analj^st interested in structural integrity is, therefore, frequently hard put to compromise both aims efficiently in arriving at a configuration, part icular^ because of the physical properties of the grain material. Whereas conventional engineering analysis usually deals with linear relations between stress and strain, grain materials are potentially nonlinear and, generally speaking, more sensitive to time dependence, including the effect of temperature. The background relating to viscoelastic analysis, including the theoretical work of Alfrey, Tsien, and Lee, is covered with special reference to grain-like configurations. The practical aspects of the elastic-viscoelastic analog}^ is brought out, and illustrated for stead3^ pressure and temperature loading on star grains. The use of previous^ developed pressure and thermal stress concentration data for propellant analysis is described, and the importance of physical property data and material representation b}^ mathematical models is discussed. Finalty, the needs for some presently lacking physical propert}^ data and a satisfactory failure criterion for grain materials are stressed in order to instigate additional work in this area.