This study investigates the ultrasonic guided wave propagation in an elastic–viscoelastic (steel–rubber) bilayer structure. 2D finite element models are developed in the frequency domain to simulate the wave propagation in the steel–rubber bilayer structure. The guided wave A0 mode is generated in the bilayer with a contact L-wave probe and detected with an out-of-plane laser vibrometer. Several wave features, such as amplitude, phase velocity and phase delay, are measured and compared to determine the characteristic changes of the A0 wave mode in the steel layer alone as well as in the bilayer structure. Studies are also performed for the bilayer structure when excited from the steel and rubber surfaces. The amplitude and phase velocity of the A0 mode are reduced in the bilayer compared to the steel layer alone. The phase velocity of the A0 wave mode in the bilayer does not depend on the viscoelastic properties of the rubber layer, rather depends only on the elastic properties of the rubber layer. The viscoelastic rubber layer in the bilayer structure does not sustain any independent wave mode; instead, it carries the A0 mode of the steel layer alone as a modified A0 wave mode in the bilayer structure. A parametric numerical study of the viscoelasticity of the rubber layer in the bilayer structure shows that the attenuation of the modified A0 mode in the bilayer is more affected by the bulk S-wave attenuation than the bulk L-wave attenuation. The rate of attenuation of the modified A0 mode in the bilayer is faster on the rubber surface than on the steel surface. A study on the A0 wave mode interaction with the interfacial disbond between steel and rubber layers is also carried out. © The Author(s) 2022.