Abstract The previous studies have shown that it is possible to obtain NbC1−x and TaC1−x single-phase, dense polycrystals during pressure-less sintering at temperatures below 2000°C. The paper presents results of investigations concerning a model description of the sintering process of the carbides using two sintering models. In order to study the sintering process of the carbides a sintering model was proposed which was a modification of the sintering model proposed by Frenkel. The model is valid for non-crystalline viscous solids in which the viscosity term was assumed to be linearly related to time. Parameters describing the sintering process of the carbides, i.e. the initial shrinkage rate α−1, the limit of the shrinkage in infinite time β−1 and the initial apparent viscosity η0 of the system were determined using the Frenkel's model. The attempt has been made to determine the mechanisms of mass transport dominating at each sintering stage according to the Kuczynski's model applied to the sintering process of the carbides. The collected data enabled full characterization of the sintering process of the niobium and tantalum carbides.