The fictionally truncated boundary must be treated properly in the seismic analysis of underground structures. In order to simplify the calculation, simplified lateral boundary, with vertical constraints and horizontal freedom, is a good choice. Based on the plane problem,a simplified lateral boundary was derived as if it was subjected to a far field shear stress state, and the rationality of the simplified lateral boundary was analyzed theoretically. Then the performance and width of the lateral boundary were evaluated through several selected benchmark numerical examples, namely the homogeneous soil layer, general thickness layered soil and thick layered soil. There are many factors influencing the width of the lateral boundary, such as the soil damping ratio, structure's scale, seismic characteristics and soil nonlinearity, whose influential degrees were studied through the dynamic time history method. It is shown that in general,the soil damping ratio and soil nonlinearity have similar effects on the width of the boundary, that is,the larger the damping ratio or the soil nonlinearity, the smaller the needed lateral boundary width,while the trend will be not too obvious when the large soil damping ratio and strong soil nonlinearity exceed a certain degree. It is also found that the structure's scale has some influence on the width of the boundary, that is ,larger size structure requires wider boundary width. The spectrum characteristics and the duration of seismic wave have great ereffect on the width of lateral boundary. 