Induced seismicity caused by underground fluid injection occurs because of pore pressure changes that lead to stress changes in the reservoir and the surrounding formations. Despite that noticeable seismic events from fluid injection is very rare, proper assessment of possible seismic events is important. The objective of this study is to develop numerical models that simulate stress changes, fault slips, and ground floor movements induced by underground fluids injection. The numerical analysis process presented in this work consists of three steps. First, stress changes around the reservoir due to fluid injection are analyzed using a FEM-BEM (Finite Element Method - Boundary Element Method) coupled model. Secondly, the stability of faults located near the reservoir is evaluated using the displacement discontinuity method. Thirdly, elastic waves caused by the fault slip is simulated using a FEM model where seismic response on the surface are calculated. A field case study is also presented to demonstrate the applicability of the numerical model developed in this work. The numerical analysis results indicate that stress concentration occurs around a boundary between the basement and sandstone beneath the reservoir. This affects the stability of existing faults in this region. As a result, when the fault is slipped, seismicity may be triggered. It is assumed that the slip is caused by stress changes in the faulted region as well as a pore pressure change in the fault, which is caused by volumetric strain changes of the fluid in the fault. A field case study based on wastewater injection in the Southwestern region of the United States where injection induced seismicity events have been recently reported, is also performed in this work. In this case study, the variation of rock strength is considered one of important factors in induced seismicity events. The novelty of our model is the ability to quantitatively assess the risk of induced seismicity due to wastewater injection, which can be also applied to other applications such as CCS and underground gas storages. Moreover, conducting risk assessment by these numerical models can improve safety of underground fluid injection operations.