This study proposes a free-form (FF) surface creation (FFSC) method to optimize the profile of a FF solar concentrator such that each incident ray is directed to a user-specified point on the solar cell surface. The light ray paths within the concentrator system are analyzed using an exact analytical model and a skew-ray tracing approach. The effectiveness of the proposed method is demonstrated numerically by comparing the irradiance uniformity performance of five concentrator systems, namely a single FF reflector (single-FF), a standard parabolic reflector with a single FF reflector (SP + FF), a single-SP reflector (single-SP), a dual-SP reflector (dual-SP) and a SP + standard hyperbolic (SP + SH). The simulation results show that the concentrator systems containing FF reflectors achieve a significantly better irradiance uniformity than those based on conventional SP and SH reflectors. (C) 2015 Elsevier Ltd. All rights reserved.