A new mathematical model describing mass and heat transport during ultrasound-assisted convective drying of a packed bed consisting of highly shrinkable small grains is proposed in this paper. The model assumes: linear volume shrinkage of grains, constant bed porosity, air incompressibility, small Biot number conditions of heat and mass exchange between grains and air. The model consists of four differential equations describing changes in the packed bed's moisture content and temperature as well as in absolute humidity and temperature of the drying air passing through the packed bed. A modified Lax-Wendroff numerical method for solving the set of model equations is proposed. Numerical simulations of packed bed drying were performed for different drying conditions. The obtained results confirm both the high impact of ultrasounds on the heat and mass exchange between grains and air and small impact of ultrasound energy absorption. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.