A mixed variational statement and corresponding finite element model are developed for an axisymmetric solid body under external symmetric loads using the updated Lagrangian formulation. The mixed finite element formulation treats the nodal displacements and stresses as the variables that can be approximated independently. The method of static condensation is used to keep some stresses across interfaces of a solid of revolution discontinuous. The stiffness matrix is transformed from semi-positive definite to positive definite. A rocket motor is composed of (1) case (2) propellant and (3) hollow air core and is modelled as an axisymmetric solid. The propellant of a rocket motor is treated as a viscoelastic material. Static and dynamic analyses are performed under (1) two opposite line loads (2) two opposite patch loads and (3) one line and one patch load combination. The modified Newton-Raphson method is used in the solutions of nonlinear algebraic equations. The analysis of free vibration is executed first and then the Newmark direct integration method is used in a transient analysis. Results of these analyses are compared with solutions obtained from different methods that are independent of the finite element method. / Ph. D.