The development of an analytical model for predicting the performance of HF lasers that result from the mixing of atomic fluorine with molecular hydrogen in continuously flowing systems is described. The model combines a temperature-dependent solution for a premixed laser system with laminar or turbulent flame-sheet mixing schemes to generate closed-form expressions for the two conditions of constant pressure (simulating a free jet) and constant density (simulating a partially confined flow). The various approximations, including a fully communicating cavity and characteristic reaction and deactivation lifetimes, are discussed. Scaling laws that relate power to the total pressure and nozzle parameters are developed. Comparison with exact numerical treatments for a wide range of conditions reveals that the model is consistently accurate to ~10%. Finally, the sensitivity of the predictions to the kinetic rate package and the utility of the model for performing parameter studies are indicated.