Summary Most of the approximate methods (Rayleigh-Ritz, iteration, etc.) for computing eigenfrequencies of structures yield upper bounds. Lower bounds are usually less easy to estimate and often present larger discrepancies from the exact values. There are cases, however, where methods of mass and/or flexibility decomposition, applicable to composite systems, readily give useful results. Stepped beams are a good case in point. Further problems of beams with variable cross sections are considered and formulas are given for the two first eigenfrequencies of symmetric beams.