Abstract: Under the natural circulation conditions, it is shown that the single phase flow instability in parallel U-tubes of steam generator (SG) can exist and the reverse flow occurs within some U-tubes, which have negative effect on nuclear power plant passive safety. In this paper, the dimensionless analysis was used to deduce the non-dimensional conservation equations and the flow instability criterion (critical Grashof number) was derived according to the linear instability analysis. The results show that for a certain U-tube, while the Grashof number is higher than the critical Grashof number, the flow in the U-tube is instable, and the reverse flow will occur. Aiming at a certain type of steam generator, the flow instability in the U-tubes was analyzed and the flow instability criterion was verified by comparing with current existing methods. The effect of inlet density on the flow instability in U-tubes was studied. The result shows that the lower the inlet density is, the easier the reverse flow happens. The conclusions can be used in the optimal design of the steam generator.