Drying is an old traditional method of removing liquid from inside material, suchas wood, food, paper, ceramics, building materials, textiles, granular products, pharmaceutical and electronic devices. The kinetics of this liquid removal depends on the material properties of the solid phase as well as on cellular structure. The aim of this project is to understand the effect of complex interaction of heat, moisture and shrinkage to create a detailed mathematical modelling to quantify the drying of a food product and tropical fruits in particular, which typically have high water content. To this purpose, in first part of the thesis, an initial simple coupled diffusion model with Fickian moisture transfer and Fourier heat transfer by Wang and Brenann [122] has been extended. A one-dimensional model is applied with the effect of shrinkage for a prediction of moisture and temperature distribution during drying. Constant physical and thermal properties are used relevant to tropical fruits. A numerical solution technique, based on the method of lines, is used with local finite difference methods approximation to the drying. The results match well with published food drying simulation studies and the anticipated final state of shrinkage in particular. To obtain a detailed understanding of simultaneous heat and liquid transfer during drying of fruits, the internal structure has to be modelled. In fruit tissue, intercellular space existing within a highly complicated network of gaseous channels can be considered as a porous medium. Guided by this, an extended model of drying, incorporating the heterogeneous properties of the tissues and their cellular structure, is recognized and simplified to represent the physical model. In this model, a distinction is made between the different classes of water present in the material (free water, bound water and water vapour) and the conversion between them. Evaluation is applied to the range of one-dimensional structures of increasing complexity: the first is an isothermal model without consideration of heat effects; the remaining have heat effects but differ in the correlated spatial arrangement of micro and macro pores. All results are given as drying curves and phase distributions during drying.