The effectiveness factor is formally determined by solving a two-point boundary value problem, often numerically. To enhance the computational efficiency in simulations of large-scale reactor systems with porous catalysts, a simple approximation formula for the effectiveness factor is often used. For some reaction rate functions, however, the effectiveness factor as a function of Thiele modulus can show multiple values or sharp changes for a small change in the modulus. In this case, single-valued approximations of the effectiveness factor may give rise to large errors. Based on the two well-known asymptotes of the effectiveness factor for small and large Thiele moduli, we proposed equations for the approximation of the effectiveness factor for up to three multiple steady states and two catalyst geometries of an infinite slab and a sphere. The proposed equations were demonstrated to be useful in estimating the effectiveness factor, particularly for the stable steady states, and also in quickly estimating the Thiele modulus range where multiple effectiveness factors should be searched. (c) 2007 Elsevier Ltd. All rights reserved.