[en] This lecture outlines in a simple way the mathematics of various cases of diffusion which have been widely used in modelling soil aeration. Simplifications of the general equation of diffusion (Fick's law) giving two possible forms of the problem: planar or one-dimensional diffusion and radial diffusion are given. Furthermore, the solution of diffusion equation is obtained by the analogy to the problem of electrical flow (Ohm's law). Taking into consideration the soil respiration process, the continuity equation which accounts for the law of conservation of mass is solved. The purpose of this paper has been to review the interrelation soil structure-air movement in waterlogged clay soils, and its consequences on plant growth and crop production. Thus, the mathematics of diffusion is presented, and then its application to specific cases of soil aeration such as diffusion in the soil profile, soil aggregates and roots is given. The following assumptions are taken into consideration. Gas flow in soils is basically diffusion-dependent. Gas-phase diffusion is the major mechanism for vertical or longitudinal transport (long distance transport); this means, with depth Z in the soil profile (macro diffusion). For horizontal transport (short distance transport or micro diffusion) which is assumed to be in X direction; in this case, the geometry of aggregates and the liquid phase are the major components of resistance for diffusion. Soil aggregates and roots are considered to be spherical and cylindrical in shape respectively. Soil oxygen consumption, Sr, is taken to be independent of the oxygen concentration and considered to proceed at the same rate until oxygen supply drops to critical levels. Thus, aeration problems are assumed to begin when at any time, in the root zone, the oxygen diffusion rate, ODR, becomes less than 30x10^-8 g.cm^-2.sec^-1, or the value of redox potential Eh is less than +525 mv