The dynamics of the railway vehicles are nonlinear and depend upon several factors including vehicle speed, normal load and adhesion level. The presence of contaminants on the railway track makes them unpredictable too. Therefore in order to develop an effective control strategy it is important to analyze the effect of each factor on dynamic response thoroughly. In this paper a linearized model of a railway wheel-set is developed and is later analyzed by varying the speed and adhesion level by keeping the normal load constant. A wheel-set is the wheel-axle assembly of a railroad car. Patch contact is the study of the deformation of solids that touch each other at one or more points