The paper deals with the psychological issues of the Russian sport in general (including internal and external, objective and subjective ones). The attitudes of the most authoritative sports experts are analyzed. Various media discuss the performance of Russians in the Olympics of the third Millennium, the role and importance of psychology in modern sport and also in preparation of elite sport athletes for such important tournaments as the Olympic Games. The paper discusses fundamental differences of psychological preparation of the Russian and foreign athletes, comparative analysis of national team performances of Russia in the summer Olympics and Paralympic Games over the past 20 years, i.e. in 1996, 2000, 2004, 2008 and 2012. The paper analyses the strongest team performances on the global level in the latest Summer Olympic games and the probabilistic prediction of the performance results in the Summer Olympics in Brazil in reference with November doping scandal in the Russian Athletics Federation associated with charges of the Russian athletes in the mass doping followed by a loud dismissal of a number of sports officials and coaches, with two Russian athletes to be disqualified and stripped of their medals of London Olympics-2012, and also a RAF member in the IAAF to be suspended, which puts into question the possibility of Russian national athletics team participating in the next Olympics. The paper outlines current problematic issues the solution of which is urgent for the 21st Summer Olympics 2016 in Rio de Janeiro, Brazil, and should contribute to a fundamental change in the psychological, spiritual, moral atmosphere not only of an individual athlete, but for all Russian sport in general.