Solution to a generalized eigenvalues interval equation is studied by d enoting the interval parameters of uncertain structure with random variables, an d a concise algorithm is presented. The interval variables are supposed to be re ctangle distribution with maximum entropy in allowable range, and the random var iables obey a uniform distribution in its definition domain on the assumption th at they are independent each other. The solution to the interval eigenvalue equa tions is achieved by using the probabilistic theory, and then a random factor me thod is applied to obtain the bounds of eigenvalues. For comparisons, the interv al variables are also supposed to be random normal distribution and the ranges o f corresponding eigenvalues are obtained. Finally, an engineering practice is em ployed to confirm the feasibility and validity of the approach.