The paper presents a generalization of the conventional analytical approach where the quasi-steady theory is utilised to evalu-ate the across-wind aerodynamic damping of slender single beam structures.This generalized theory considers the variation of structural and aerodynamic parameters along the structural height,together with the nature of the vertical wind profile and mode shapes.Closed-form solutions for typical uniform and tapered tall buildings are given.A numerical application on a prototype tall building shows that the conventional method may be oversimplified,which results in incorrect predictions of the aerodynamic damping.