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Cob is an earthen construction technique used to build monolithic load-bearing walls. Mainly of vernacular nature, remaining cob buildings can be found throughout Europe as well as in other specific locations around the world. The aim of this paper is to evaluate the available material models’ suitability for the modelling of cob’s structural behavior in one of the most commonly used FEM software in the market. The stress-strain graphs obtained and the failure mechanisms observed after a simple compression and diagonal compression experimental campaign in cob wallettes were replicated using three different material constitutive models, namely, MISO, CONCR, and DMGE/DMGI. Furthermore, a mesh size sensitivity analysis was performed following a mesh refinement approach. MISO could reproduce the pre-peak behavior of cob and principal stresses could be used as an indication of the opening of cracks. On the other hand, it did not capture the softening post-peak behavior of the material. CONCR provided quite accurate pre-peak behavior results and peak strength values. Moreover, it was possible to plot the opening of cracks and those plots agreed with the experimental results. Nevertheless, as CONCR is suitable to reproduce brittle failures, it did not capture the long deformations characteristic of cob. Finally, the DMGE/DMGI proved to be inaccurate to reproduce both pre-peak and post-peak behavior. Although parameters could be calibrated to obtain the appropriate peak strength, neither stresses nor did strains correspond to what was observed in the experimental campaign.