Gas-solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, and nucleation model. These models give two coupled partial differential equations (CPDEs). In this work an integral transformation and subsequent finite element method is used for solving the coupled partial differential equations of these reactions. In each mesh the Rayleigh-Ritz method is applied. Finally the results of this work are compared with the existing numerical solutions and experimental data successfully. (C) 2008 Elsevier B.V. All rights reserved.