Abstract: The thermophysical properties of working fluids in the near-critical pressure region are highly sensitive to pressure and temperature, leading to a significant risk of hydrodynamic instability when ultra-supercritical boilers operate in the supercritical section of this region. To ensure the stability and safety of ultra-supercritical boilers during deep load cycling, a mathematical characterization method for the occurrence mechanism and dynamic response characteristics of density wave oscillations in water walls under supercritical pressure conditions is established based on conservation equations. Using the frequency-domain method, the boiler tube section is divided into three regions—liquid, vapor-liquid mixture, and vapor—according to the physical properties of the working fluid. After applying a small linear perturbation and performing Laplace transformation, the transfer function of the boiler tube section is obtained. A critical heat flux prediction program is developed based on MATLAB and C language, and system stability is analyzed using the Nyquist criterion from automatic control theory. A 660 MW ultra-supercritical pulverized coal boiler is selected as the research object, with a focus on its operation in the near-critical pressure region under supercritical conditions. The critical heat flux and dynamic response characteristics of the longest loop in the lower furnace under this condition are calculated. The critical heat flux for this loop is determined to be 274 kW·m^-2, and the actual operating point is far from the critical heat flux point, meeting safety criteria. A systematic study is conducted to examine the effects of various parameters, including pressure, inlet subcooling, inlet mass flow rate, heat flux, and tube length, on the transient response characteristics of the boiler when key operating parameters—such as thermal load, inlet enthalpy, inlet flow rate, and outlet pressure—undergo step changes. The results indicate that higher boiler operating pressures lead to longer recovery times for system stabilization but smaller parameter disturbance amplitudes. Higher inlet enthalpy and heat flux result in shorter recovery times but larger disturbance amplitudes. Increased inlet mass flow rates shorten recovery times and reduce disturbance amplitudes. Longer tube lengths prolong recovery times and amplify disturbance magnitudes. Overall, increasing pressure and mass flow rate enhances system stability, whereas raising inlet enthalpy, heat flux, or tube length undermines stability. The findings of this study provide theoretical guidance and practical reference for the safe peak-shaving operation of ultra-supercritical boilers within the supercritical zone of the near-critical pressure region during deep load cycling.