The main purpose of this paper is to present both the natural frequencies and the first critical loads of tapered columns. The ordinary differential equation governing the free vibration for tapered columns under compressive axial force is derived. Three kinds of cross sectional shape are considered in the governing equation. The Runge-Kutta method and determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. Additionally, the bisection method is used to determine the critical loads. In numerical examples, the effects of compressive axial force on the natural frequencies of tapered columns are investigated varying the end conditions. The first critical loads of tapered columns are determined on the basis of dynamic concepts. The first critical loads of tapered columns are determined on the basis of dynamic concept. The effects of cross sectional shapes are shown and some typical mode shapes are also presented.