Abstract This paper presents a probabilistic algorithm for determining the effect of initial state variation on the dynamic stability of power systems. Variation of operating conditions due to the uncertainties in load and generation is represented by the statistical attributes of nodal voltages. Expectation and covariance are employed to describe the distribution nature of random variables. The expected coefficient matrix in the state space equation is corrected by the second-order covariances. The solution gives the probabilistic distributions and conditional probabilities of eigenvalues. The proposed algorithm is examined on a two test systems.