Leakage in the pressure sensing lines of a nuclear power plant may lead to problems such as deviations in pressure readings. To detect potential sensing line leakage faults in a timely manner, this study proposes using the Burg method to estimate the power spectrum of the sensor noise signal and to extract typical frequency characteristics of the pressure measurement system, which can be used to evaluate the health status of the sensing line. By establishing a lumped parameter mathematical model for the pressure measurement system and leakage faults, the signal response under normal conditions and leakage conditions of the measurement system was simulated in MATLAB. The trends of signal spectral characteristic changes and measurement result deviation changes under different leakage sizes were obtained, which preliminarily verified the feasibility of using power spectrum estimation methods to monitor leakage in pressure sensing lines. The research lays the foundation for blockage monitoring of pressure sensing lines in nuclear power plants.