To overcome the prohibitive computational cost associated with detailed mechanistic models for fuel cell stacks, we derive an efficient computational strategy based on thermal and electrical decoupling of cells. The conditions that allow for decoupling are discussed and verified with a non-isothermal model considering two-dimensional conservation of mass, momentum, species, energy, charge, and electrochemistry for a 10-cell proton exchange membrane fuel cell (PEMFC) stack. The derived strategy allows for simulation of large stacks comprising hundreds of cells at a low computational cost and complexity; e.g., for a PEMFC stack comprising 500 cells, the decoupled algorithm takes less than 30 min to solve and requires only 1 GB of random access memory.