The axisymmetric extensional modes of free vibrations of a thin prolate spheroidal shell separate into two classes, one class with displacements perpendicular to the meridional planes and one class with displacements in the meridional planes. This paper concerns itself with the former, the torsional modes. The differential equation for the mode shapes, obtained by application of Hamilton's principle, is found to be satisfied by single prolate spheroidal angle functions of the first kind, and the transcendental frequency equation is readily solved with the aid of tabulated eigenvalues. Numerical and graphical nondimensional results are presented for the first eight modes.