Rail corrugation is a pathology that appears in almost all railroads, causing a progressive corrugation at the head of the rail that leads to an increase of costs for track maintenance. The most common way to deal it is the use of corrective measures (grinding). However, in the present study aims to investigate the implementation of a preventive measure to prevent its appearance. To do this, it has analyzed the influence of elastic material placed under concrete plate in the vibratory behavior of a track through mathematical modeling. The results show a reduction in the amplitude of the vibration and a modification of their frequencies.