The article presents a review of publications on the realization of the constitutional rights of the accused to the trial by the court with the jury participation. The conclusion is made about the need for further research with regard to legal positions of the constitutional Court of the Russian Federation. The article considers the jurisdiction of criminal cases to the jury on a personal basis. The author provides the data on the reduction of the jury cases in the court jurisdiction. In accordance with article 31 of the Code of Criminal Procedure of the RF, accused minors and women could not file a motion for the jury trial. In addition, these criminal cases must be transferred for consideration from the regional court to the district court. It violates the constitutional principle of equality of citizens before the law and the courts. The analyses is given to the decisions of the Constitutional Court of the RF about jurisdiction of criminal cases to the Grand jury. The position of the Constitutional Court of the RF on this issue is contradictory. The court declared the deprivation of the minors Deprivation of the minors of the right to the jury trial was declared consistent with Constitution of the RF by the Constitutional Court of the RF while deprivation of women of the right to the jury trial was declared inconsistent with the Constitution of the RF. The article formulates a proposal for the appropriate amendments in the Code of Criminal Procedure of the RF.