Abstract: The article contains the critical analysis of the procedure of formation of a preliminary list of candidates to the jury. The author studies such its drawback s as the lack of guarantees of the random sampling principle observance and its isolation from the sides. The author develops the procedure of a preliminary list of candidates formation which should allow the sides and the superior court to control the observance of the law, whereas the current legislation doesn’t contain the guarantees of a list of candidates formation on the base of the random sampling principle. The author carries out the comparative analysis of the methods of selection of candidates and generalizes the judicial practice on the issues of formation of a preliminary list of candidates to the jury. The author substantiates the following suggestions: 1) to legislate the selection of candidates to the jury with the use of computer programs; 2) to vest the sides with the right to attend the procedure of formation of preliminary lists; 3) to record the procedure and the results of selection of candidates.