To clarify the characteristics of non-uniform flow of gas through layered burdens of ore and coke, flow equations of continuity and motion were solved numerically taking account of the geometrical effect of a bed. The results are compared with that predicted by an approximate solution. A mathematical-kinetic model for determining the distributions of process variables over the region from the top to the melting level of blast furnace with the horizontal or the inclined layers of burdens is developed in consideration of the uneven gas flow. By the use of this model, the longitudinal and the radial distributions of process variables in an existing blast furnace in Japan were calculated with the aid of a digital computer. Computed results show that the process variables and the melting level change remarkably over the cross-section of the furnace and that the patterns of these distributions are similar to the results observed by other investigators.