Annoying vibration waves generated by passing trains highlight the necessity for the assessment of the effects of railways on their environment. Dynamics of structures close to railway tracks is amongst such important issues. Contrary to the past studies, this article proposes a modeling method that is totally based on the idea of discrete masses. It considers three major parts as the accomplices causing undesirable oscillations including the track, the ground bed, and the structure in the vicinity of the track. The ground bed is considered as an elastic half space subdivided into discrete masses. It facilitates modeling for the track systems that may include any deliberate discontinuity, such as voids and trenches, in the ground bed that supports the railway track. Such discontinuities arise from engineering perception and are useful in controlling the spread of noise and vibrations. A \MATLAB" based computer program is written to solve the motion equations in the time
domain. The proposed method provides  flexibility in modeling. Variety of track loading and wave propagation scenarios can be simulated without the need to rebuild the model. This method can be practically used when seeking remedies for controlling the levels of unwanted vibrations in the structures.