This article is deals with the history modular arithmetic, based on the rest classes calculus system «Restklassenarithmetik» (RCCS), or Modular Arithmetic, regarding its creation and development in the USSR. Characteristics of the USSR first modular super-computers: “Т-340А”, “К-340А”, “Diamond (Алмаз)” and “5E53” and their development history are briefly considered. A brief analysis of the weakening of interest in the modular arithmetic in the USSR and its subsequent resumption of the Russian Federation is given. It also provides information on holding the 2006 special commemorative Scientific International Conference “50 Years of Modular Arithmetic” in the town of Zelenograd, Moscow.