In the given work the problem of quality of generating of random numbers is studied. The purpose of work - to find out opportunities and qualitative characteristics of various generators of random numbers; to test their work; to compare and estimate quality of most often used generators. Work consists of three basic parts: The first part is devoted to questions of generating of random numbers, namely: what is the random number where sequences of random numbers are used, what ways of their reception. The big attention is given a question of qualitative characteristics of generators of random numbers, their classification is resulted. The greatest attention is given program gauges pseudo random numbers, and the information on hardware devices of generating of casual sequences has fact-finding character. In the second part it is spoken about testing generators of random numbers. In this part the basic methods of testing are considered, the most interesting sets of statistical tests are described. The third part - research. The purpose of researches - to allocate from the most popular program generators of random numbers (standard functions of various programming languages: Basic, Pascal, Delphi, C ++), the generator with as much as possible high quality of generating. In the end of work conclusions about the executed researches are given. Texts of the used programs, full the table of data, schedules and diagrams are presented in appendices.