The effect of external mass transfer on the steady state multiplicity is studied. We analyzed a complex system of heterogeneously catalytic reactions in an isothermal CSTR, where the concentrations in bulk fluid are different from those on the surface of nonporous catalysts. The system is proved to admit multiple steady states by a zero eigenvalue analysis and a set of parameters generating multiplicity is constructed. Numerical result shows the hysteresis and bistability occur for certain range of external mass-transfer coefficients. As increasing either the flow rate or the feed concentration of a reactant, it is necessary to increase the mass-transfer coefficient to maintain the multiplicity.