Expressions for the spectra of gravity and magnetic anomalies due to a vertical right circular cylinder can be written in terms of a Bessel function and the sum of two exponentials. From the zeros of the amplitude spectra, which are the zeros of the Bessel function, an estimate of the radius of the cylinder can be obtained. The depths to the top and to the bottom enter as exponents of the exponential terms and can be evaluated by taking ratios of the spectra at several frequencies. The density or the intensity of magnetization can then be easily estimated. For the magnetic case the epicenter of the cylinder can be obtained from the slope of the phase spectra. The method has been tested on anomalies of various cylinders and was found to give good results.