A finite element analysis is developed for nontopochemical reduction of a porous iron oxide pellet. The reduction kinetics are essentially the same as those used by Trushenski, Li and Philbrook. However, several novel features arise in the present analysis. The computational technique used in this analysis provides an explicit way of calculating gas profiles for each step of the computations. To a limited extent multicomponent gas mixtures (either carbon monoxide, carbon dioxide and inert gases; or hydrogen, steam and inert gases) can be accomodated as the reducing agent. A corresponding analysis for direct reduction of iron oxide in a countercurrent shaft furnace assumes adiabatic conditions to prevail in the furnace as opposed to the usual isothermal assumption. The analysis assumes steady-state operation of the furnace, and plug flow of gas and solid. Profiles of gas and solid temperatures, degree of reduction of iron oxide pellets, bulk gas and solid compositions are calculated.