Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water cooled reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN has been developed employing supercritical water properties to carry out the steady-state and linear stability analysis of a SCW natural circulation loop (SCWNCL). The conservation equations of mass, momentum, and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure, and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been benchmarked against published results. Then the code has been extensively used for studying the effect of diameter, heater inlet temperature, and pressure on steady-state and stability behavior of a SCWNCL. A separate computer code, NOLSTA, has been developed, which investigates stability characteristics of supercritical natural circulation loop using nonlinear analysis. The conservation equations of mass, momentum, and energy in transient form were solved numerically using finite volume method. The stable, unstable, and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behavior of loop, predicted using nonlinear analysis has been compared with that obtained from linear analysis. The results show that the stability maps obtained by the two methods agree qualitatively. The present paper describes the linear and nonlinear stability analysis models and the results obtained in detail.