During high-solids anaerobic digestion (HS-AD) of the organic fraction of municipal solid waste (OFMSW), an important total solid (TS) removal occurs, leading to the modification of the reactor content mass/volume, in contrast to ‘wet’ anaerobic digestion (AD). Therefore, HS-AD mathematical simulations need to be approached differently than ‘wet’ AD simulations. This study aimed to develop a modelling tool based on the anaerobic digestion model 1 (ADM1) capable of simulating the TS and the reactor mass/volume dynamics in the HS-AD of OFMSW. Four hypotheses were used, including the effects of apparent concentrations at high TS. The model simulated adequately HS-AD of OFMSW in batch and continuous mode, particularly the evolution of TS, reactor mass, ammonia and volatile fatty acids. By adequately simulating the reactor content mass/volume and the TS, this model might bring further insight about potentially inhibitory mechanisms (i.e. NH3 buildup and/or acidification) occurring in HS-AD of OFMSW.