COMPRESS uses the Rayleigh method to determine the fundamental natural frequency of vertical pressure vessels. The "Rayleigh - Ritz Summation" procedure is described in many vibration textbooks. A vessel specific application of the method is presented in the paper "Vibrations of Vertical Pressure Vessels" by C. E. Freese. Freese's paper is available on Codeware's web site at www.codeware.com/support/papers/freese.pdf.