Accelerators and beam transport systems are the most widely used in various fields of fundamental and applied science. This leads to the need for construction of correct models of the corresponding objects and processes. In this paper we consider the problem of forming a beam with a given distribution. Note that similar requirement to the beam occurs in circular accelerators, and in the beam transport systems for various fields of physics, chemistry, biology and so on. Special attention is paid to the development of effective mathematical methods and computer programs to modeling of control systems to ensure the necessary requirements to the beam.