A simple analytic solution for Tonks-Dattner resonances in a cylindrical plasma with a parabolic density profile is derived using the approximation of pure electrostatic radial waves. For other density distributions the resonances are calculated using numerical integration of a second order differential equation. Results are compared with the scalar pressure theory derived by Parker et al. (1964), and with Dattner's (1963) experimental results. Excellent agreement is obtained over the full range of conditions used in these publications.