A fin structure for cooling cold-heat refrigerant and another fin structure (slender grooves or the like) constituting a working gas flow passage are formed on the outer and inner surfaces of the heat exchange housing constituting a low-temperature heat exchanger by a lost was casting method so that these fin structures are formed integrally with the heat exchange housing. In addition, a fin structure and another fin structure constituting a working gas flow passage are integrally formed on the outer and inner surfaces of a high-temperature side heat exchanger (heat rejector). Accordingly, the heat exchangers of a Stirling machine can be manufactured in a simple structure by the lost wax casting method, whereby the workability can be enhanced and the manufacturing cost can be reduced. In addition, the precision for the workability can be enhanced, and the heat exchange efficiency and the reliability can be enhanced.