Cloud-based manufacturing (CBM) has recently been proposed as an emerging manufacturing paradigm that may potentially change the way manufacturing services are provided and accessed. In the context of CBM, companies may opt to crowdsource part of their manufacturing tasks that are beyond their existing in-house manufacturing capacity to third-party CBM service providers by renting their manufacturing equipment instead of purchasing additional machines. To plan manufacturing scalability for CBM systems, it is crucial to identify potential manufacturing bottlenecks where the entire manufacturing system capacity is limited. Because of the complexity of manufacturing resource sharing behaviors, it is challenging to model and analyze the material flow of CBM systems in which sequential, concurrent, conflicting, cyclic, and mutually exclusive manufacturing processes typically occur. To address and further study this issue, we develop a stochastic Petri nets (SPNs) model to formally represent a CBM system, model and analyze the uncertainties in the complex material flow of the CBM system, evaluate manufacturing performance, and plan manufacturing scalability. We validate this approach by means of a delivery drone example that is used to demonstrate how manufacturers can indeed achieve rapid and cost-effective manufacturing scalability in practice by combining in-house manufacturing and crowdsourcing in a CBM setting.