The integration of new technologies and changing of principles of power system's control and operation have led to the necessity for increasing the level of details of the data and representation used in the models for planning power system future perspectives. Because of this fact, the computation burden of the traditionally used Monte Carlo simulation technique (MCS) has become significant even in terms of long term planning. Analytical method that allows to speed up calculations of generation adequacy indices such as the risk of exceeding tie lines capacity constraints by power flows is proposed in the article. The proposed approach is based on Lagrange multipliers method applied for random values. In accordance to the test calculations the proposed method requires less computation time and enough accurate in comparison to MCS.