Multiple free-piston stirling-cycle machine modules are connected together in double-acting configurations that may be used as engines or heat pumps and scaled to any power level by varying the number of modules. Reciprocating piston assemblies oriented in balanced pairs reduce vibration forces. There are no buffer spaces. Linear motors or generators are packaged inside piston cavities entirely within the module working spaces. The external heat-accepting and heat-rejecting surfaces in one embodiment are directed along inward-facing and outward facing cylinders, and in another embodiment along parallel planes, simplifying thermal connections to the external heat source and sink.