As one of the most common engineering geological phenomena caused by earthquake, the liquefaction of saturated sand is also one of the main causes of major earthquake disasters. Due to the complexity of causes and the severity of disasters, the liquefaction of saturated sand has always been an important subject in the field of soil dynamics and geotechnical earthquake engineering. In this paper, based on the platform OpenSees, the numerical simulation were carried out on four constitutive models for sand. The response results of the four models in terms of acceleration, displacement, excess pore water pressure, shear stress-strain, and mean effective stress path under the action of cyclic dynamic load were analyzed and compared. The research results showed that: (1) Sand shows a certain amplification effect on the input acceleration, and there are some differences in the amplification effect for different models; (2) Stress Density model is prone to permanent deformation under cyclic dynamic load; (3) Under cyclic dynamic load, the strength of PDMY model and CycLiqCPSP model gradually decreases until it completely lost; (4) Stress Density model and Manzari Dafalias model show obvious dilatancy effect under cyclic dynamic load. The research results have important theoretical value for the numerical simulation of sand liquefaction, thus providing a reference for the liquefaction simulation of saturated sand and the selection of constitutive models for sand.