A constitutive model for the stress-strain-time behavior of municipal solid waste (MSW) that accounts for waste degradation has been developed. The model is developed within the critical state soil mechanics framework. The model decomposes the total strain into a time-independent elasto-plastic strain and a time-dependent plastic strain. The time-independent strain, including both the elastic part and the plastic part, is characterized by the ellipsoidal yield surface of the Modified Cam-Clay model using the normality condition and the law of associated flow. The time-dependent strain consists of a mechanical creep part and a biodegradation part. The mechanical creep part is evaluated by Taylor’s secondary compression equation, the normality rule, and the Modified Cam-Clay yield surface. Biodegradation strain is assumed to be isotropic and is characterized by first order kinetics and mass that decays loss exponentially with time. The decrease in the compressibility of MSW as it biodegrades is accounted for by changing the slope of normal consolidation line and the value of the specific volume at the reference pressure based upon the mass loss due to decomposition. A method for obtaining the model parameters is provided.