The analysis of stress and strain in an orthotropic heterogeneous linear viscoelastic cylinder which has a burning inner boundary and which is subjected to a time‐dependent internal pressure, has been worked out. The assumptions of isothermal conditions and infinitesimal strains are consistently made and the conditions of a quasistatic plane strain are adopted. Numerical solution for an orthotropic heterogeneous viscoelastic cylinder is established and which was anticipated to be quite stable. The established solution can be reduced to that of a homogeneous orthotropic cylinder. As special cases from the general problem, solutions for an isotropic compressible cylinder and an isotropic incompressible cylinder can also be derived. Numerical examples have been worked out to illustrate the influence of anisotropy, heterogeneity, and viscosity on the deformation of a burning cylindrical grain in a solid propellant rocket. The results for both short‐time and long‐time behavior are presented for a relaxation function of a form similar to that obtainable from a seven‐parameter Maxwell model which has been shown to represent the rheological behavior of a filled elastomer fairly well.