In many cases, an oil production rate increase can result in excessive sand production, casing collapse and expensive workover jobs. In this thesis the strength of the rock formation around casing perforations is studied by means of the theories of poroelasticity and poroplasticity. Three plasticity models, Tresca, Mohr-Coulomb and Quadratic yield criteria, are considered, with the emphasis for each model being on the use of strain-softening plasticity for calculating inelastic stresses. Hemispherical and long cylindrical cavities are modeled to simulate the perforation cavity. Both associated and nonassociated flow rules are implemented to describe the plastic stress-strain relations. The maximum allowable drawdown and stress distribution in the formation are determined for fluid flowing into the cavity. Effects of formation properties and boundary conditions on cavity collapse are studied and compared. The effect of permeability change in the formation is also studied and analyzed. Calculations based on the strain-softening model are compared with published experimental results. The difference between ground surface pressure and bottom hole pressure in the unsteady-state reservoir problem is studied by an electric analog method. Transient pressure effects can cause premature casing collapse since large pressure gradients exist during the first few time steps. Based on the nearly-steady-state method, a safety chart is proposed to indicate how to decrease wellbore pressure safely.