A modular plate and shell heat exchanger in which welded pairs of heat transfer plates are tandemly spaced and coupled in parallel between an inlet and outlet conduit to form a heat transfer assembly. The heat transfer assembly is placed in the shell in order to transfer heat from a secondary to a primary fluid. Modules of one or more of the heat transfer plates are removably connected using gaskets at the inlet and outlet conduits which are connected to a primary fluid inlet and a primary fluid outlet nozzle. The heat transfer assembly is supported by a structure which rests on an internal track which is attached to the shell and facilitates removal of the heat transfer plates. The modular plate and shell heat exchanger has a removable head integral to the shell for removal of the heat transfer assembly for inspection, maintenance and replacement.