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It has been observed by performing simple and diagonal compression tests of cob wallettes that the structural behavior of cob is highly nonlinear. This paper presents the results obtained of the simulation of cob’s nonlinear monotonic behavior using two well-known finite element commercial packages. Pros and cons of different available constitutive material models are identified and discussed. Concrete (CONCR) and Concrete Damaged Plasticity (CDP) are considered as the constitutive material models that provide the more satisfactory results reproducing cob’s nonlinear monotonic behavior when using ANSYS and ABAQUS, respectively.