A one-dimensional cylindrical cure model was developed to describe the curing process of an axisymmetric filament wound composite structure. For a specified cure cycle, the cure model can be used to calculate the temperature distribution, the degree of cure of the resin, and the resin viscosity inside the composite case. Solutions to the cylindrical cure model were obtained numerically using the finite element technique. The cylindrical cure model was verified by measuring the temperature distribution in a small 5.75 inch graphite - epoxy test bottle. The data were compared with the results calculated with the computer code for conditions employed in the tests. Good agreement was found between the data and the results of the computer code. The error between the experimental data and the results of the computer code was less than 10 %. A cure cycle optimization problem is formulated for the curing process using a calculus of variations approach. The optimum cure cycle should tailor the temperature in the composite such that a uniform temperature and degree of cure distribution is achieved in the composite while minimizing the reaction exotherms and thermal lag. Cure simulations of an one inch thick graphite - epoxy composite case predict a minimization of the reaction exotherms and the thermal lag. The the final process time needed to achieve uniform degree of cure and uniform temperature distribution in the composite is also predicted. The resultant cure cycle appears to approach the boundary temperatures specified as limits on the cure cycle temperature. / Master of Science