Covers installed over waste disposal sites are used to control water and gas exchanges with the surrounding environment. One example involves covers built to limit oxygen flux to sulphidic mining and milling wastes, which can be the source of acidic leachate. In this paper, the authors present an approach to evaluate oxygen flux and its controlling parameters, the effective diffusion coefficient De and reaction (consumption) rate coefficient Kr. A laboratory experimental procedure to determine these two parameters simultaneously is described, and the proposed interpretation method is presented with a few sample results. New analytical solutions are developed to calculate oxygen flux through covers with capillary barrier effects (CCBE). The proposed solutions are compared with results ensuing from a numerical treatment of Fick's laws. Specific applications of these analytical solutions are presented and discussed.Key words: unsaturated soils, covers, capillary barrier, Fick's laws, oxygen diffusion, acid mine drainage, analytical solutions, numerical solutions.