A structural synthesis methodbased on state space mathematics is described. This state space method (SSM) is used to model the free vibrations of a refrigeration compressor shell. Five models that progressively approximate compressor shell geometry are analyzed. The results are compared with experimental data and bounded analytical solution. The SSM is then employed to investigate the dependence of compressor shell natural frequencies on the location of the welded seam, the shape of the end caps, and the introduction of curvature in the cylindrical body. Some of the claims made by earlier investigators have been critically examined. These studies can lead to a stiffer design of the compressor shell.