Abstract: Loose sandy soil can undergo static liquefaction under undrained conditions and the onset of instability is within the failure line, and this kind of instability is called diffusion instability. In recent years, some studies have shown that failure can occur under drained conditions. The constant shear drained (CSD) tests can be performed to investigate this drained instability. A key point of CSD tests is to control the error of deviating stress for getting reliable results in experiments. The discrete element method is used to simulate the CSD tests of sand with different densities under different shear stress levels. Based on the Hill's second-order work criterion, the possible model for instability in CSD tests are divided into two types. Both the modes of instability are observed in DEM simulations. The influences of initial void ratio and shear stress level are analyzed on instability under CSD loading path. The numerical results indicate that the samples with lager void ratio are easy to collapse, and the higher the shear stress level, the faster the instability occurs. The slope of instability line (IL) associated with the initial void ratio is also discussed in details, and a unified method is proposed to analyze sand instabilities under both drained and undrained stress paths. Finally, the numerical results from this study are compared with test ones of several kinds of sands.