To investigate the variation patterns of ultrasonic nonlinear response characteristics at the contact interface of high-voltage cable terminals, the stress-strain relationship of silicone rubber material was measured to explore the material’s inherent nonlinearity. An ultrasonic nonlinear detection experimental system was constructed, and ultrasonic detection experiments were conducted to validate the correlation between interface pressure and ultrasonic nonlinear coefficients, as well as to explore the causes of nonlinear responses at the contact interface. The results indicate that the nonlinear response at the contact interface originates from both the material’s inherent nonlinearity and the contact interface nonlinearity. The higher-order harmonic components in the echo signals are primarily attributed to the contact interface nonlinearity. As the interface pressure increases, the relative increase in the ultrasonic nonlinear coefficient decreases progressively from 25.10% to 1.60%. The reduction in the fundamental wave amplitude follows a sequence of 1.89%, 1.75%, 1.84%, 5.22%, 4.73%, 0.94%, and 14.38%, while the trend of the second harmonic is similar to that of the fundamental wave. Both the fundamental and second harmonic amplitudes exhibit a decreasing trend as the interface pressure increases. The experimental results provide a reference for the feasibility of applying ultrasonic nonlinear detection methods to the engineering assessment of interface pressure in high-voltage cable terminals.