Sand production is one of the most frequent and serious problems observed during the production of an oil well completed in weak sandstones. This phenomenon can cause wellbore plugging, surface and rise equipment abrasion, casing collapse and environmental problems derived from the disposal in surface of contaminated sands. On the other hand, for reservoirs of low productivity, that produce oil of high viscosity, a limited sand production increase the productivity of the well. In the studies for sand production prediction, it is of basic importance to define a consitutive model capable of reproducing the stress-strain behaviour of the sandstones and the failure mechanisms that causes wellbore instability. This is the central focus of the present work. In order to represent the behaviour of the rock masses, models based in Cosserat continuum were used. Elastoplastic models (associated/not associated) under that theory (Bogdanova-Bontcheva and Lippmann) were implemented. Initially, basic concepts related to the understanding of the phenomenon of solid production are presented. A review of the theory of generalized Cosserat continuum is presented, the elastoplastic model of Bogdanova-Bontcheva and Lippmann is described, together with details of the computational implementations. Finally, analyses of well geometries with the implemented Cosserat based elastoplastic models are shown,identifying the failure mechanisms.