A multi-cell electrochemical reaction cell structure for a flow battery or fuel cell having a plurality of cells electrically connected in series or parallel. A first housing has a pair of mating end plates assembled together, each forming a plurality of recesses in which one of the cells is received. One of the end plates has a projection along its perimeter and the other one of the end plates has a groove along its perimeter. The projection is configured to fit within the groove in a mating relationship to seal the housing when the end plates are engaged with each other. A second housing is a tubular shell in which a plurality of tubular flow cell units electrically connected in parallel are housed. Catholyte flows in the tubular flow cell units and anolyte flows in the tubular shell.