A method and apparatus for converting radiation power, especially solar radiation, into mechanical power. A piston is provided that is movable in a cylinder accompanied by the formation of a variable-sized working chamber. During a compression stroke, the piston is used to press a working medium, accompanied by a reduction in the size of the working chamber, into a radiation absorber/heat exchanger that is disposed directly in the working chamber, receives radiation energy, and essentially completely accommodates the working medium when the working chamber is at a minimum. During a working stroke, the working medium, which is compressed by the reduction in size of the working chamber and which is heated up by absorbing thermal energy from the radiation absorber/heat exchanger, is used to move the piston, upon expansion of the working medium, into a position that enlarges the working chamber. At least a portion of the working medium is exchanged following the working stroke and prior to a subsequent compression stroke.