Precast concrete structures have been considered due to various advantages in the construction industry by the recent decades. On the other hand, these member joints make problems such that so many failure modes have been observed during earthquakes because of collapses in these connections. So, the joints can be considered as one of the key points in the seismic behavior of the structures. Among these joints, significant emphasis must be applied to beam-column connection in design and performance. The objective of this thesis is to study the behavior of a type of precast concrete moment resistance beam-column connection under lateral loading and to compare the performance of this connection to the monolithic connection system by the use of finite element method and nonlinear analysis in ABAQUS application. The precast connection is in the form of a continue beam cross throughout the column. The lower column longitudinal bars have been crossed through the existing holes in the beam and are anchored in a special type of sleeve in the lower part of the top column. It is necessary to explain that sleeves are a type of mechanical joints for connecting the bars. In addition, to study the performance of the connections, the behavior of rebar joints with sleeves must be considered. Thus, the joint of rebar by the use of sleeve is modeled firstly and after the accuracy is ensured, numerical analysis of the desired connection is performed using the result obtained from this phase. In the next phase of this thesis, dedicated to the modeling of both monolithic and precast concrete connections, outputs from numerical analysis are verified using the experimental results. Also in this phase, the level of consideration of anchorage slip phenomena effects of reinforcement embedded in concrete in the models is examined. In the third phase of this research, study and comparison of the desired precast concrete moment resistant connection and the monolithic connection’s behavior (under various tensile and compressive axial loads on the column) is performed. The results of the numerical analysis indicate very good performance of precast connection in terms of stiffness, strength and ductility, compared to the similar monolithic connection. On the other hand, the results of modeling reveal that a change in axial load from compression to tension, in addition to decreasing stiffness, strength and ductility of both connections, cause the change of fracture mode. In case of applying pressure on column, failure of models is due to plastic hinges at the face of column in the beams and yielding of transverse reinforcements in this region. While in presence of tensile overload, longitudinal reinforcement of the beams at plastic region yield initially (like in pressure) and at the end of lateral loading, longitudinal reinforcement of the columns will yield.