Kuhn-Tucker approach and its dual have been proposed to the demand system estimation when there are non-negativity bindings. However, empirical researchers have been struggling two decades in applying this method into practice due to: (1) the difficulty in derivation of a coherent econometric model, and (2) the cumbersome evaluation of high order probability integrals needed in parameter estimation. In this paper, we avoid the above two issues by using the Amemiya-Tobin demand system approach and the simulation procedure to evaluate the probability integrals. An AIDS model is estimated and the elasticities are obtained that are impossible to achieve when using Kuhn-Tucker approach. The model is applied to an analysis of Canadian household food demand.