This paper is the first part of the theoretical work devoted to electrical cross effects in biporous media with ice inclusions. The fine-pored part of the medium is saturated by the electrolytic solution. A heat and mass transfer problem is formulated for an elementary cell of the medium on basis of diffusion mechanism. An equation set is proposed for finding the temperature, pressure, concentration, and electric potential fields. All the heat and mass flows through the cell depend on the cross thermodynamical forces. In the closed system the electric polarization induced by temperature gradient depends on the hydroconductivity of the fine-pored medium, the solution concentration and the ice content. At the low solution concentration and the high hydroconductivity the thermoelectric potential difference may be as great as 150 mV K-1. In the open system the ice presence has no effect on the diffusion potential difference induced by concentration gradient. (C) 2008 Elsevier Ltd. All rights reserved.