It has been suggested that modes of vibration of solid elastic spheres, such as those used in the calibration of echo sounder systems, can be affected by the manner of suspension. This hypothesis is investigated in the context of reported experimental calibration trials with the SIMRAD EK500/120-kHz echo sounder. In these, as many as four different spheres were used: 23- and 30.05- mm-diameter spheres composed of electrical grade copper and 33.2- and 38.1-mmdiameter spheres composed of tungsten carbide with 6% cobalt binder. Theoretical target strengths are computed for each sphere for the reported measurement conditions for a series of cases in which single vibration modes remain unexcited. The computed target strengths are compared with the corresponding experimental values. The working hypothesis is not supported by the data.