A high temperature solid oxide fuel cell generator produces electrical power from oxidation of hydrocarbon fuel gases such as natural gas, or conditioned fuel gases, such as carbon monoxide or hydrogen, with oxidant gases, such as air or oxygen. This electrochemical reaction occurs in a plurality of electrically connected solid oxide fuel cells bundled and arrayed in a unitary modular fuel cell stack disposed in a compartment in the generator container. The use of a unitary modular fuel cell stack in a generator is similar in concept to that of a removable battery. The fuel cell stack is provided in a pre-assembled self-supporting configuration where the fuel cells are mounted to a common structural base having surrounding side walls defining a chamber. Associated generator equipment may also be mounted to the fuel cell stack configuration to be integral therewith, such as a fuel and oxidant supply and distribution systems, fuel reformation systems, fuel cell support systems, combustion, exhaust and spent fuel recirculation systems, and the like. The pre-assembled self-supporting fuel cell stack arrangement allows for easier assembly, installation, maintenance, better structural support and longer life of the fuel cells contained in the fuel cell stack.