Weakly consolidated reservoirs are prone to sand production problem, which can lead to equipment damages and environmental issues. The conditions for sand production depend on stresses and properties of rock and fluid. Accurate sand volume estimation is, however, still a challenging issue, especially for reservoirs in weak formations. The weak reservoirs containing viscous or heavy oil are mainly discovered in shallow depths in Kazakhstan, with moderate temperature and pressure. Many prediction models developed for open-hole completions where the reservoir materials usually possess certain strength are not applicable for the local reservoirs where the materials are significantly weaker even if casing is used to support the wellbore with oil produced through the perforation tunnels. In this context, a prediction model was proposed where the volume of the produced sand was estimated as the volume of the plastic zone of the failed materials surrounding the perforation tunnels. The model assumes an evolving truncated conical shape for the damage zone and takes into account stress distributions and shear failure in this zone. Then, the proposed model was used to estimate sand volumes in 20 wells during oil production with sequential increase of flow rates. The predictions match well with the measured sand volumes in a local oil field. Finally, a sensitivity analysis was conducted on the model performance. It shows that the permeability of the plastic zone was the most significant controlling factor in the prediction results.