The existence Of two well-defined structures in the parenchymatic tissue of apples (the flesh) gave us the opportunity to study the significance of the initial structure oil mass transfer rates of two apple varieties, Kim (Sweden) and Granny Smith (Argentina) when subjected to osmotic dehydration. Our results verified the importance of the initial structure for osmotic processing responses. Knowledge of the properties of the tissue and the solution penetration into the intercellular space, permitting rw to explain the kinetics found. Shrinkage properties such as volume changes, bulk density, particle density and porosity, have been studied macroscopically for both structures, inner (close to core) and outer (close to skin) and presented as a function of water content in a manner similar to air drying practice. A comparison with shrinkage properties observed in air drying is attempted.