When performing calculations to assess reliability of hydraulic structures of cascades of hydroschemes on the basis of probabilistic methods, the necessity to simulate random natural-climatic phenomena producing loads and effects on hydraulic structures arises. In particular, statistical series of random quantities of such important natural-climatic phenomena, obtained by direct measurements in dam sites of hydroschemes of Dnieper cascade of hydroelectric stations, are considered: annual maximal flood discharges, annual maximal ice thickness, annual lowest average monthly temperatures, annual maximal amplitudes of average monthly temperatures. Each of the enumerated natural-climatic phenomena is characterized by presence of close correlation connections between random quantities when passing from one hydroscheme of the cascade to another. The necessity to consider correlation connections requires construction (simulation) of joint distribution law of random quantities system. Principles of construction of joint distribution law of system of random quantities satisfying normal distributions are widely presented in the present-day literature and do not cause difficulties. In the case when distribution laws of random quantities system do not satisfy the normal ones, approaches with transformation of the initial statistical series of data into the normal law by the use of corresponding substitutions are proposed.