This is the first of three papers on modelling and simulation of crossflow grain dryers. This paper focuses on the model development while the second and third papers concentrate on applications of the model to study design modifications and optimization of the dryer design and operation respectively. Earlier studies have established a physical chemistry and diffusion model for grain drying. This knowledge is now applied to the development of a Distributed Parameter Model (DPM) of the deep bed grain drying process and a simulation of crossflow com dryers. The conservation and rate equations have been normalized and the characteristic groups have been identified. The resulting set of non-linear partial differential equations has been numerically integrated by the method of centred differences. The DPM is presented in this paper. A comparison of the DPM with experimental data and the Michigan State Crossflow Dryer Model (MSM) was made. Both models predict similar results when similar equilibrium moisture content values are used.