The optimal shape of a Pfiuger column is determined by using Pontryagin's maximumprinciple (PMP). The governing equation of the problem is reduced to a boundary-value problemfor a single second order nonlinear differential equation. The results of the analysis problem areobtained by Spectral method. Necessary conditions for the maximum value of the firsteigenvalue corresponding to given column volume are established to determine the optimaldistribution of cross-sectional area along the column axis
