Passage of the train wheels induces ground-borne vibrations at the rail-wheel interface, where the main contribution is due to the axle loads moving on irregular track and wheel interface. These vibrations can cause problems such as the compaction and settlement of the foundation soil of the structures nearby, liquefaction of the soil or discomfort of people, just to name a few. Therefore predicting and controlling such phenomena is critically important for the design and operation of the railways. These vibrations are modeled using many different methods existing in the literature. In this paper we analyze the effects of groundwater depth and ground inclination angle on those vibrations using a random vibration model, where the elastic rail-soil system is modeled as a Winkler foundation. We examine the effects of changing fully saturated groundwater levels and changing ground inclination angles on such vibrations. We relate the groundwater depth and ground inclination angle parameters with the stiffness of the Winkler model using Terzaghi's, Vesic's and Bowles's bearing capacity formulas. The common 5-axle and the 6-axle tram load configurations and different train speeds of 30 km/hr, 40 km/hr, 50 km/hr are used in our implemented model. It is shown that the decrease in groundwater depth and/or higher ground inclination angle can significantly change the peak and rms vibration velocity and acceleration levels, both for the 5-axle and 6-axle configurations and all three different train speeds. We present exponential and exponential-trigonometric fit curves to the results of the implemented random vibration model, which can be used to model the approximate changes in the ground-borne vibration velocity and acceleration levels due to different groundwater depth and different ground inclination angles. We also discuss our results and their applicability.