The stabilization process in municipal solid waste (MSW) is inherently complex. In the short term, waste has an immediate elastic response due to surcharge loading. Long-term stabilization involves two time-dependent components: an initial secondary mechanical settlement phase (i.e. creep) and, later, a thermally dependent biodegradation phase. Two composite compressibility models were used to simulate settlement and compared to field data from a MSW landfill located in Ste. Sophie, Quebec, Canada. One model was based on the work from Marques et al. (2003) and another on the theory of viscoelasticity. The models were developed using COMSOL Multiphysics to simulate the MSW mechanical response and were examined through a parameter optimization study. Both models achieved correspondence with the field data for prediction of short-term and long-term settlement. The parameters achieved for both model types are all within acceptable limits from literature for MSW.