A new approach to the numerical solution of normal mode problems in underwater acoustics is presented, in whichthe corresponding normal mode problem is transformed to the problem of solving a dynamic system. Three applica-tions are considered: (1) the broad band normal mode problem; (2) the range-dependent problem with perturbationproportional to the range parameter; and (3) the evolution of the normal mode with environmental parameters. Anumerical simulation for a broad band problem is performed, and the calculated eigenvalues have good agreement withthose obtained by the standard normal mode code KRAKAN.