Numerical studies have been carried out to investigate supercritical flow instabilities in a CO2 natural circulation loop. For the steady state and dynamic analyses of the loop under supercritical conditions, a single-channel, one-dimensional model is developed. In this model, equations for the conservation of mass, momentum and energy are discretized using an implicit finite difference scheme. A computer code called FIASCO (Flow Instability Analysis under SuperCritical Operating conditions) is developed in FORTRAN90 to simulate the dynamics of natural circulation loops with supercritical fluid. Results obtained for the stability boundary substantially deviate from the results reported by previous investigators, and thus contradict some of the reported findings. The disagreement in results is most likely due to the undesirable dissipative and dispersive effects produced from the large time steps used in previous studies, thereby leading to a larger stable region than those found using smaller time step. Results presented here suggest that the stability boundary of a natural circulation loop with supercritical fluid, is not confined to the near-peak region of the (steady state) flow-power curve. Additional and more extensive experimental data are needed to resolve the differences between results obtained here and those reported earlier. However, results obtained for the range of parameter values used in this investigation always predict the stability threshold to be in the positive slope region of the (steady state) flow-power curve. Parametric studies for different operating conditions reveal the similarity of stability characteristics under supercritical conditions with those in two-phase flows.