In this study, we consider a component procurement planning problem where the procurement amounts of components are determined under assemble-to-order systems with demand uncertainty. In the problem, procurement amount of each component is decided before the demands of finished products are known and after the demands are identified the assembly amounts of the finished products are decided. In this study, the objective function of the problem is minimizing the total costs which are composed of purchase and inventory costs of the components and the backorder costs of the finished products. We assume that the uncertain demand information is given as multiple scenarios of the demands, and we propose procurement planning methods based on stochastic models which considering the multiple demand scenarios. To evaluate the performances of the proposed methods, computational experiments were carried out on the proposed methods as well as benchmarks including a method based on deterministic mathematical model and a heuristic. From the results of the computational tests, the superiorities of the proposed methods were shown.