The case of the eigenvalue problem of quadratic matrix beam is proposed. The method permitting to calculate all eigenpair of the matrix beam. With this aim the generalized eigenvalue problem is reduced to the linear problem. Then the modificated successive approximations method for calculation the eigenvalues and eigenvectors is used. It permits us, using the information got from all fulfilled iterations, to obtain the first eigenpair and all the next ones more quickly. Some numerical examples are considered.