A mathematical method is presented for determining stresses in solid propellant rocket grains due to pressurizatio n, steady thermal gradients, and uniform propellant shrinkage. The type of solid propellant grain considered is a long cylinder containing a longitudinal perforation with an arbitrary number of identical star points of general shape. The external boundary of the propellant grain is bonded to a circular-cylindrical motor case. The propellant has constant mechanical and thermal properties and is in a state of plane strain. Linear elasticity theory and complex variable methods are used to formulate a general stress problem for a doubly connected region that has a star-shaped internal boundary and a circular external boundary and is subjected to steady thermal gradients and uniform boundary pressures. This problem is solved approximately by considering a related problem for an infinite plane with a star-shaped hole. Effects of bonding the external boundary to an elastic case are deduced approximately by superposition. A general stress program for a digital computer is described, and example computations testing the validity of the assumed approximations are made. The method is found to provide a practical means of analyzing stresses in solid propellant grains.