A step-function reaction rate model is used to study the problem of steady, 1D, planar two-reactant pre-mixed flames. The analysis yields leading order solutions for the flame structure and the dependence of the flame speed on reaction and transport parameters. The results for the flame speed reproduce the same scaling obtained using activation energy asymptotics. Two analytical solutions are derived for the cases of stoichiometric and far from stoichiometric flames. These solutions constitute the first closed-form solutions of the flame structure at non-unity Lewis numbers for the reactants. Comparisons between numerical solutions based on an Arrhenius reaction rate with the analytical solutions show an excellent agreement. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.