Abstract: The theoretical performance of a conical solar concentrator with a cylindrical receiver is studied in this paper. The calculation formulae of concentration ratio and sun-tracking accuracy for single-section conic concentrator were deduced. The irradiated length on the receiver was determined and the axial concentration distribution along its surface was expressed mathematically. Three factors of concentration ratio, tracking precision and material utilization ratio were analyzed and it was found that 45° is the most appropriate half apex angle for a single-section conic concentrator. It is indicated that the single-section conic concentrator exists the contradictions among the un-shaded area of the aperture, concentration ratio and the length of the receiver. To overcome such a disadvantage, the multi-section conic concentrator is considered and designed, of which, it is feasible to increase the un-shaded area of the aperture and concentration ratio without changing the receiver length. Meanwhile, the design of multi-section conic concentrator could be flexible.