SUMMARYThis paper is concerned with the mechanics and computation of the performance of a high energy chemical laser of the HF type. The analysis requires solving the viscous, compressible supersonic flow equations which are coupled to the chemical and optical characteristics of the flowing gas media. A finite element method is chosen for performing the computation.The physical system simulated in the work consists of the supersonic mixing of the two flows; one flow consists of hydrogen gas whereas the second flow is rich in fluorine gas. Perpendicular to the flow, an optical cavity provides for reflection and amplification of radiation characteristic of the output of the HF laser system.The HF system achieves a population inversion of the HF molecule as a result of the chemical reaction between H2 and F. This reaction also provides heat which couples with the fluid mechanics as an influence on the flow field. This paper will discuss the nonlinear nature of the problem, will present the finite element method used to solve the problem, and will compare results with others who have used finite difference methods for solution.