This paper deals with the elastica and buckling loads of the nonlinear elastic tapered cantilever columns subjected to an axial load at the free end. The column cross section is rectangular, where the width and depth vary linearly with the column axis. The column material is nonlinear elastic, which obeys the Ludwick’s constitutive law. The ordinary differential equations governing the elastica of buckled column are derived and solved numerically for computing the elastica and buckling loads. Parametric studies for the annealed copper, N.P. 8 aluminum alloy and steel columns are conducted