A theoretical model for a beam-forming device, based on the "lens-axicon" pair with a truncated central part is constructed. The device is distinguished by the fact that it gives a more uniform distribution of energy in the irradiation circle. Analytical relations, describing the form of the distribution as a function of the radius of the central part and the other parameters of the apparatus, are derived. The relations obtained pertain to both the cases of truncated and untruncated central part of the system, and reduce to known limits as the radius of the central truncated part approaches zero. Nomograms of the energy distribution over the irradiation circle are presented. Analysis of the results obtained shows that the relations derived are useful for solving applied problems that require highly uniform energy distribution in the irradiation circle.