This paper compares numerical methods for solving the competitive storage model. Since storage implies an inequality constraint, the solution methods must be considered carefully. The model is solved using value function iteration, and several projection approaches, including parameterised expectations and decision rules approximation. Using a penalty function approach to smooth the inequality constraint, perturbation methods are also applied. Parameterised expectations proves the most accurate method, while perturbation techniques are shown inadequate for solving this highly nonlinear model. The endogenous grid method allows rapid solution if supply is assumed to be inelastic.