An industrial scale falling film reactor (FFR) using gaseous SO3/ liquid Alkylbenzene –as operating system- is analyzed for multiplicity and stability. The analysis has shown that up to 5 steady state solutions may exist. The existence of a highly multiplicity states is explained by the coupling between absorption and reaction. The system kinetic parameters have found to play an effective role on the stability behavior. An analytic solution is found for a special case of the liquid reactant in excess, this solution is performed by using eigen analysis. A mathematical procedure is also introduced to estimate the bifurcation points.