A low-cost beam-down concentrating solar tower (BCST), equipped with three linear Fresnel heliostat modules, corresponding beam-down concentrator, and the central receiver with cavity absorber, is introduced and theoretically analyzed in this paper. A conical cavity receiver is applied to reveal the effect of geometric configuration on solar propagation of the BCST. The detailed derivation process of sun-tracking formulas for the BCST is implemented. In addition, detailed numerical models for thermal behaviors of the conical cavity receiver with the BCST concentrator, on the basis of the three-dimensional CFD method, have been developed. The objective of this paper is to evaluate optical and thermal performances including the heat flux distribution on the absorber surface, heat losses, as well as thermal efficiencies, thereby providing useful data for practical solar process heat application. Numerical prediction shows that the operational volume flow rate between 1.0 and 2.0 m³ h⁻¹ is suggested to the CR using the HTF (water) under the geometry and operational conditions in this paper.