This paper proposes an effective ultrasonic detection methodology for assessing the damage state of cylindrical structures. The methodology depends on the interaction between a bounded ultrasonic beam and the cylinder. First, the theoretical derivation of the scattered sound field generated by a bounded ultrasonic beam incident obliquely onto a cylinder is presented. Next, by means of FE simulations and experimental verification, we demonstrate that when the bounded ultrasonic beam emitted by the transmitter is obliquely incident upon the cylinder at either the first or second critical angles, as defined within this study, the early initiation of damage results in a significant increase in the received sound pressure amplitude detected by the receiver positioned symmetrically relative to the transmitter. Specifically, the simulation results indicate that a mere 5 % decrease in the elastic modulus of the cylinder correlates with a staggering 447.88 % surge in the received sound pressure amplitude at the first critical angle. Experimental evidence also demonstrates that for varying states of impact-induced damage of the cylinder, the received sound pressure amplitude detected by the symmetric receiver exhibits highly sensitive characteristics when a bounded ultrasonic beam is incident at the first critical angle onto the cylinder. This approach represents a significant advancement over traditional ultrasonic detection techniques, combining the reliability and stability of linear ultrasonic methods with the sensitivity for early damage assessment provided by nonlinear ultrasonic techniques. The proposed assessment method holds great promise in providing fresh insights for inspecting cylindrical structures in practical applications.