Eigenfunction convergence characteristics of the finite element method and the Rayleigh-Ritz method with quasicomparison functions (RRMM) are compared. The RRMM has previously proved to be superior in comparing eigenvalue convergence characteristics. The importance of studying natural mode convergence is associated to the fact that the general response of a structure is a linear combination of these characteristic functions; in other words, accurate structural response attainment demands accurate structural modes in the analysis. It is shown that in this case the RRMM also produces superior results. A refined definition of quasicomparison functions is advanced. © 2007 - IOS Press and the authors. All rights reserved.