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The quality of the natural vibrations of specific bacteria is investigated using a shell model which accounts for the elastic properties of the membrane and the associated viscosities of the cytoplasma and the surrounding fluid. The motion of the membrane is approximated in terms of the distribution of internal forces over the shell thickness, which is assumed to be much less than the size of the cell. Flexural moments and intersecting stresses are neglected. Using experimentally obtained values for the membrane properties, high-quality resonances are predicted for several types of bacteria which have radii greater than 5 microm. Viscous shear waves are the main source of energy dissipation as has been previously reported in other studies on the natural oscillations of red blood cells, drops, and bubbles. Implications for the acoustic mediated destruction of bacteria are discussed.