An approach based on the principle of energy is proposed to study the free flexural vibration of chordwise doubly-tapered cylindrical shallow shells. The variations in shell thickness are linear and symmetric. This topic is of practical interest, but one on which no previous work has been conducted. The analysis is performed using an efficient computational method based on the Ritz minimum energy approach. The in-plane and transverse displacement amplitude functions of the shells are approximated by sets of pb-2 shape functions with unknown coefficients. The pb-2 shape functions are basically a set of admissible functions composed of the product of a set of mathematically complete two-dimensional orthogonal polynomials and a boundary kinematically oriented basic function. The basic function is defined by the product of the equations of continuous piecewise boundary expressions of the shell planform each raised to an appropriate basic power corresponding to a free, simply supported or clamped edge, respectively. These pb-2 shape functions comply with the kinematic boundary conditions of the shells at the outset. Three classes of different shell configurations and boundary conditions are studied with selected mode shapes presented. A study on the ignoring of tangential inertia has shown little effect on the frequency response. However, the trend reveals a higher effect is evident as the shell curvature increases. The effects of symmetric thickness variation are reflected in the tabulated data, as well as the mode shape figures. Since no data for a doubly-tapered cylindrical shallow shell can be found in the open literature, the results presented in the current study can be used for future reference and comparison. © 1994.