Abstract A theoretical analysis of a variable area rocket based combined cycle engine with and without simultaneous mixing and combustion is presented. The flowfield is solved using a steady, quasi-one-dimensional, inviscid control volume formulation with combustion effects included via a generalized equilibrium calculation. Compression augmentation is shown to be sensitive to the equivalence ratio within the primary rocket chamber, where ejector section performance is greatest at both low and high equivalence ratios but near a minimum at stoichiometric conditions. The thrust generated by the RBCC engine compared to that generated by the same rocket in isolation can be increased by as much as 12% at constriction ratios of between 45% and 50%. Thrust augmentation is also shown to vary with equivalence ratio, where for a fixed geometry the maximum thrust is generated at equivalence ratios slightly below unity.