A mathematical model is developed to simulate the response of a kaolin clay sample when subjected to convective, convective-microwave and convective-infrared mode. This model is proposed to describe heat, mass, and momentum transfers applied to a viscoelastic medium described by a Maxwell model with two branches. The combined drying methods were investigated to examine whether these types of drying may minimize cracking that can be generated in the product and to know whether the best enhancement is developed by the use of infra-red or microwave radiation. The numerical code allowed us to determine, and thus, compare the effect of the drying mode on drying rate, temperature, moisture content and mechanical stress evolutions during drying. The numerical results show that the combined drying decrease the intensity of stresses developed during drying and that convective-microwave drying is the best method that gives a good quality of dried product. (C) 2014 Elsevier Ltd. All rights reserved.