Most of the building materials are considered porous, and composed of solid matrix and pores. In the pores, the moisture can be existed in two phases: liquid and vapor. Thus, the mass balance equation is comprised of various moisture driving potentials that translate the movement of the different existing phases occupying pores and the hygroscopic behavior of a porous construction material. This study suggests to resolve a hygrothermal mathematical model of heat and mass transfers in different porous building materials by a numerical investigation. Thereby, the evolution of temperature and moisture content fields has been processed. So, numerous series of hygrothermal calculation on several cases of wall are exposed. Firstly, a case of monolayer wall of massive wood has been treated. In this part, we have compared the numerical solution of the model on one and two dimensions and the effect of dimensional space has been evaluated. In the second case, three building materials (concrete, wood fiberboard and wooden insulation) are tested separately with the same boundary conditions and their hygrothermal behavior are compared. The evaluation of the exchange of heat and air at the interface between the wall and the interior ambiance is carried., {"references":["J. Zhang, X. Zheng, L. Chen, Y. Sun, Effect of residual oil saturation on hydrodynamic properties of porous media; Journal of hydrology Volume 515, 16 July 2014, Pages 281–291.","L. Fengzhi, L. Yi, L. Yingxi, L. Zhongxuan, Numerical simulation of coupled heat and mass transfer in hygroscopic porous materials considering the influence of atmospheric pressure, Numer. Heat Transfer B 45 (3) (2004) 249–262.W.-K. Chen, Linear Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993, pp. 123–135.","B. Remki, K. Abahri, M. Tahlaïti, R. Belarbi, «Hygrothermal Transfer In Wood Drying Under The Atmospheric Pressure Gradient», International Journal of Thermal Sciences, Article in press, 2012.","Fortin, O. Millet, G. De Saxe, Numerical simulation of granular materials by an improved discrete element method, Journal of Computational and Applied Mathematics 168 (2004) 207–213.","L.Z. Zhang, Numerical study of heat and mass transfer in an enthalpy exchanger with a hydrophobic–hydrophylic composite membrane core, Numer. Heat Transfer A 51 (7) (2007) 697–714.","Y. Jen, Liu, Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies. International heat and mass transfer, vol.34. No.7, pp.1747-1754, 1991.","J. Fan, X. Cheng, Y.S. Chen, An experimental investigation of moisture absorption and condensation in fibrous insulations under low temperature, Experim. Therm. Fluid Sci. 27 (2003) 723–729.","W. Chang, C. Weng. 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