Criteria for the overturning stability of tall slender structures such as chimneys and towers are developed. They are expressed in terms of structural geometric parameters and the spectral pseudo-velocity of the ground motion. The development is based on a simplified cantilever beam model and Lagrange's formulation where the system's deformations are expressed in terms of generalized coordinates. Selected examples and numerical studies demonstrate the use of the criteria as well as the role that each one of the most significant geometric, inertia and spectral parameters plays in the overturning stability of towers and chimneys.