The convective drying of a food product whose dehydration occurs under large deformation is studied. A numerical model is proposed for solving the heat and water mass transfer phenomena for cylindrical samples while including shrinkage. It is assumed that no porosity appears during drying. The finite volume method is applied, and mesh boundaries move with the dry matter. No information about the product's mechanical properties is required; shrinkage is predicted from geometrical considerations only. The approach is illustrated for the case of yacón samples, whose reduction in volume can reach 90 % after a few hours of drying. Previous work with a convective dryer pilot unit under controlled air temperature and relative humidity is considered, firstly in identifying key parameters related to the volume reduction and to the water diffusivity in the product, secondly in assessing the drying kinetics as predicted by the model.