Railway trains or mass rapid transit systems are the major public transportation tool for most major cities. In order to fully utilize the highly valued limited space in business districts, while making the commercial benefits brought by flowing passengers, the stations of underground mass rapid transit systems are often built adjacent to office or residential buildings, or even integrated with the commercial buildings. As such, many highly populated cites have encountered the noise and vibration problems of various levels on the building floors as the trains pass by. Concerning the ground vibration induced by moving trains, most of the studies focus on the responses induced only by the quasi-static load. Only few consider rail surface irregularity. However, it is well known that rail irregularity can generate high-frequency vibrations and noises that cannot be ignored in practice. As such, the effect of random irregularity will be investigated in this study In the previous studies related to rail irregularity using PSD curve, equal spacing is adopted in selecting the wavenumbers from the PSD curve. In this thesis, an improved approach is proposed for constructing the rail irregularity from the PSD curve, resulting in reasonable results with less computation time. The purpose of this study is to simulate the ground vibration induced by moving trains by considering the random surface irregularities of the rail based on a 2.5D finite/infinite element approach (Y. B. Yang & Hung, 2001, 2009). A parametric study is performed to investigate the effects of train speed, rail irregularity properties and other vehicle parameters on the soil responses. Some of existing numerical and in-situ measurement results obtained from the literatures are used for comparison with those obtained from present approach. In the end, a problem implemented with a floating slab isolation device is also evaluated, which will provide some useful reference for further application of the floating slab track in practice. The results from this study indicate that the response of the soil in velocity and acceleration will be amplified significantly once the rail irregularity is taken into account.