Abstract: A composite exponential stress-strain model of municipal solid waste(MSW) is proposed based on the large-scale consolidated drained triaxial tests.Few parameters are contained in this model and each one has specific physical meaning.It can not only reflect the non-linear characteristics of the stress-strain curves for MSW within small strains,but also the apparent strain-harden characteristics of the stress-strain curves for MSW within larger strains.This model is incorporated into the explicit finite difference program FLAC by the Fish language and verified by numerical modelling of triaxial tests.Finally,A vertical landfill expansion case is analyzed using this model,and the mechanical settlement and lateral deformation of the old landfill and the strain of the intermediate liner induced by the expanded MSW loads are evaluated.It shows that the calculated results using the composite exponential model are almost between those using the Mohr-Coulomb model and the Duncan-Chang model.The tensile strain of the intermediate liner may cause tension cracks in the compacted clay liner.