In order to process a product in a semiconductor back-end facility, a machine needs to be qualified, first by having product-specific software installed and then running test wafers through it to verify that the machine is capable of performing the process correctly. In general, not all machines are qualified to process all products due to the high machine qualification cost and tool set availability. The machine qualification decision affects future capacity allocation in the facility and subsequently affects daily production schedules. To balance the tradeoff between current machine qualification costs and future potential backorder costs due to not enough machines qualified with uncertain demand, a stochastic product–machine qualification optimization model is proposed in this article. The L-shaped method and acceleration techniques are proposed to solve the stochastic model. Computational results are provided to show the necessity of the stochastic model and the performance of different solution methods.