The envisaged decarbonization of the European power system introduces complex techno-economic challenges to its operation and development. Demand flexibility can significantly contribute in addressing these challenges and enable a cost-effective transition to the low-carbon future. Although extensive previous work has analyzed the impacts of residential and commercial demand flexibility, the respective potential of the industrial sector has not yet been thoroughly investigated despite its large size. This paper presents a novel, whole-system modeling framework to comprehensively quantify the potential economic benefits of flexible industrial demand (FID) for the European power system. This framework considers generation, transmission and distribution sectors of the system, and determines the least-cost long-term investment and short-term operation decisions. FID is represented through a generic, process-agnostic model, which however accounts for fixed energy requirements and load recovery effects associated with industrial processes. The numerical studies demonstrate multiple significant value streams of FID in Europe, including capital cost savings by avoiding investments in additional generation and transmission capacity and distribution reinforcements, as well as operating cost savings by enabling higher utilization of renewable generation sources and providing balancing services.