A number of various empirical formulas describing power spectral density of across-wind load at vortex excitation depending on flow conditions, range of Reynolds number, and lock-in phenomenon or its absence can be found in the literature. The aim of this paper is to demonstrate on the basis of the author's own mathematical models of across-wind load on a slender structure of circular cross-section at vortex excitation, that the correlation function and, subsequently, the power spectral density of this load can be described by universal formulas of two functional parameters which should be determined experimentally. Depending on the values of these parameters, the power spectral density of the analysed load can be of wide-band character (as for the Fung's spectrum), more or less narrow-band character (as for the spectrum of a Gauss curve-type), or in a particular case, of δ-Dirac spectrum type.