The paper presents a new method of load flow calculation in which the known node powers are treated as random variables. The unknown node voltages are assumed to be normally distributed and therefore only the average values and the second order moments should be calculated. These are calculated from the average values, variances and covariances of the node powers. The probabilistic load flow equations have been led out from the quadratic deterministic load flow equations and they are quartic. The deterministic equations have 2w−1 solutions forw-nodes and therefore the probabilistic equations should have at least the same number of solutions. In hitherto literature only a single solution of probabilistic load flow equations is studied. In this paper the original method for finding all solutions is presented. The analysis of load flow equations for 2-node power system is performed.