A generalized mathematical model for the packed bed electrode（PBE）was developed to describe the two-dimensional distributions of overpotential，reactant concentration and current density in the electrode.The model included the influences of lateral dispersion and vertical convection in the packed bed between electrode feeder and membrane，and was in a form of coupled elliptical and parabolic nonlinear partial differential equations.The model was solved by using Adomian decomposition method(ADM）to obtain the approximate analytic solutions，and the solving procedure was presented.Furthermore typical computation examples of the two-dimensional distributions in PBE were given by figures to show the distribution nonlinearities.The prediction of the model would provide a theoretical idea for the design or operation optimizing of PBE，and the presented method might also be used for the analysis of heterogeneous catalysis engineering system.