Conceptual design of scroll expander and scroll compressor for 10kW-class Stirling engine utilizing solar energy as heat source has been carried out to estimate the applicability of scroll mechanism for Stirling cycle. CO2 was chosen as working fluid, since it has lower expansion index and higher density among probably usable gases. Gas temperature at the expander inlet was set at $700^{circ}C$, and that at the compressor inlet was at $40^{circ}C$. System efficiency reached maximum at the pressure ratio of about 2.5, and the peak efficiency increased with increasing high side pressure. Due to safety concern, the pressure condition of 6 MPa/2.5 MPa was chosen as design condition. Orbiting scroll members for the expander and compressor were designed to have double-sided structure in order to reduce the overall scroll size and to cancel out the axial gas forces acting on the orbiting scroll base plate. By parametric study on the scroll profile, smaller possible size for the scroll members was obtained. With the shaft speed of 3600rpm, the shaft output of the designed scroll expander was calculated to be 45.4kW, while input power for the scroll compressor was 34.5kW, yielding 10.9kW for the output power of the Stirling engine. System efficiency was estimated to be about 7.3%, and overall efficiencies of the scroll expander and compressor were around 84.1% and 88.3%, respectively.