Grate-firing technology is one of the commonly used technologies for municipal solid waste incineration, which recovers energy and largely reduces the volume of the solid wastes for landfilling. In grate-fired incinerators, the solid wastes are packed in the fuel bed on the grate, where the major heterogeneous conversion takes place. A proper modeling of the fuel conversion process in the bed not only benefits an in-depth understanding of the in bed incineration but also facilitates the freeboard simulation. In this paper, a comprehensive model is developed to simulate solid wastes incineration in a packed bed, which advances the state-of-the-art with corrected boundary conditions, homogeneous reactions, and calculation method for pyrolysis products. The model is first validated by a simplified analytical problem. Then, the model is validated in detail by a dedicated experimental study in literature, in which the pyrolysis and gas combustion front and the subsequent char oxidation front both propagate from the bed surface to the grate due to the abundant oxygen availability in the fuel bed. The model also outperforms a latest modeling study in literature for reproducing the same experimental study. Finally, a model-based parametric study is conducted to investigate the effects of solid waste particle sizes and solid waste incineration in high-altitude areas. This paper also clearly explains the methods to transfer the packed-bed model to travelling grates and to accommodate the different waste fractions in real municipal solid waste, in order to make the model applicable to travelling grate-firing of real municipal solid wastes.