The acoustic behavior of the three‐dimensional cavities of musical instruments can be studied using the acoustical finite element method. For some cases, one‐ and two‐dimensional finite element models may be used, resulting in more efficient computations and a simplification of the input. The 1‐D model is used for long, cone shaped cavities found in flutes, woodwinds, and brass instruments. Guitars, violins, and instruments with a small, but variable, change in height can be studied by the 2‐D model. Analytical models incorporating elemental geometries with lossy behavior have been used in the past for the quasi 1‐D case of woodwind instruments. A 1‐D finite element program was used for similar problems where the axisymmetric cavity was long with respect to its cross section. Tone holes are included in the model by using empirically determined impedance functions applied as boundary conditions. A 2‐D finite element program was written which incorporates the height of the cavity as a parameter at the nodes. The procedure correctly predicts frequencies and mode shapes of cavities with gradual changes in height. Limitations for the permissible rate of change in height are demonstrated.