Analytical formulae are developed for estimating the amplitudes of the vibrations generated in railway tracks by wheels and rail discontinuities or by unevennesses on their surfaces. Rails are assumed to be supported elastically on concrete sleepers by resilient rail-pads inserted between them. The elasticities and the masses of track materials and those of the roadbed are also taken into consideration. It is shown that after an impulse is applied to the track, not only is a vibration with a comparatively low natural frequency generated, but also traveling waves with higher frequencies, and the latter propagate lengthwise along the track or downwards into the roadbed. With the assumption that the power spectral density of the unevennesses on the rail surface is in proportion to the third power of the wavelength, or to (wavenumber) -3, the amplitudes of the vibrations in railway tracks supported by rail-pads and roadbeds with various magnitudes of elastic constants are analyzed and the values for each one-third octave band are estimated. The velocity of the vibration takes on a maximum value for the band with a center frequency of 63 Hz, which corresponds to the resonant frequency of the system composed of the wheel and the track. As the frequency increases beyond this value, the velocity of the vibration takes on a second maximum value at a frequency of about 1000 Hz. These estimates are compared with the data obtained from field measurements and reasonably good correlations are found between them.