The basic objective of the present study is to investigate the influences of foundation parameters, orthotropy of materials represented by elastic moduli ratio, axial wave parameter, and circumferential wave number on three eigenfrequencies. Dynamic equilibrium equations and frequency equation are developed, and the eigenfrequencies are calculated. It is found that the foundation modulus primarily affects the radial mode eigenfrequency and has no effect on torsional and longitudinal modes, whereas the shear modulus does have influence on radial as well as tangential modes of vibration, though the effect on radial mode frequency is more dominating. The elastic moduli ratio chiefly affects the radial mode in a manner similar to that of a foundation modulus. When the shell rests on a Pasternak foundation, the lowest eigenfrequency vs circumferential wave-number characteristics do not have the well-known dip, and the minimum frequency occurs when the circumferential wave number is zero for all values of axial wave parameter.