A modular plate and shell heat exchanger in which welded pairs of heat transfer plates are placed in the shell in order to transfer heat from a secondary fluid to a primary fluid. The heat transfer plates are removably connected using gaskets to header pipes which are connected to a primary fluid inlet and a primary fluid outlet nozzle. The header pipes are 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 plates for inspection and replacement.