The experience of the 25 years operation of two concentrators of solar energy (CSE) of 2.8 and 5.0 m diameter manufactured by gluing plane facets of thin glass onto metal radio antennae convincingly demonstrates their technical and economic efficiency. Besides (or in addition to) simplicity of manufacturing and the possibility to achieve temperatures up to 2000 K and more, there is one more undoubted advantage of such concentrators: it is possible to get a focal spot with rather uniform distribution of the irradiance. The problem of determining the plane facets' optimum configuration and the structure of their arrangement on the CSE surface which guarantees forming a focal spot of the given dimension is solved by this work. Perfect geometric configuration of the facets and paraboloid is assumed. The working zone of the facets reflecting the incident solar radiation at the circular focal spot is approximately an ellipse. Trapezoid is an optimum configuration for the facets taking up a minimum area and ensuring the maximum use of CSE surface. A system of equations is obtained for calculation of a CSE structure with annular packing of the facets. The results of calculations for the 1.8 m and 15 m diameter concentrators are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.