A combined analytical and experimental study is presented to demonstrate that the four‐pole parameters of a truncated, thin conical shell, under axial excitations, may be accurately obtained by applying membrane shell theory. A general calculation procedure is described, and the numerical results are applied to determine the mechanical impedances of shell‐mass systems, and then compared with test data for three shell models with semivertex angles 0°, 15°, and 30° over a frequency range from 20 to 600 cps. The exce lent agreement indicates that the four‐pole parameters calculated through the present analysis are adequate for vibration analyses, if the input excitation frequency is appreciably lower than a theoretical singularity, on the frequency spectrum inherent to the membrane shell theory. If the excitation frequency is near or above this singularity, a more accurate bending shell theory must be used.