A cellular tissue is an heterogeneous, porous, chaotic medium which can be represented by a subdivision of a 2-D domain into irregular, convex polygons, known as a Voronoi tessellation, on which some polygons are randomly defined as cells and the remainder as pores. The model is used to predict the effective thermal conductivity, k*, of fruit tissues at different moisture contents, taking into account the expected morphological changes undergone by the material during drying, and the properties of cells and pores which are assumed to have the polygons representing them. At any stage of the dehydration process, the fraction of total area occupied by polygons playing the role of pores equals the porosity of the actual sample at the corresponding water content. This is done either by simply substituting cells by pores or by shrinking the cells and enlarging the pores as drying proceeds. The variational principle associated with the conduction problem leads to the calculation of upper and lower bounds for k*. The procedure is applied to the case of apples and pears, giving good results when compared with experimental data. Predictions using the shrinking cells approach, however, yield better results than the substitution one.