Abstract <p>The present study is carried out within the framework of a semi-analytical computer model. The model is based on the solution of a three-dimensional boundary value problem concerning the interaction of the acoustic field generated by an air-coupled ultrasonic transducer with a composite plate made of fiber-reinforced pregs. The investigation focuses on the influence of composite’s anisotropy and the tilt of the non-contact transducer on the directivity diagrams, frequency response, and dispersion properties of the guided waves excited in the plate. The wave field is described by the solution of the coupled problem for the system source–acoustic-medium–composite-plate obtained in the form of the inverse Fourier transform path integrals of the waveguide Green’s matrix and source parameters. The residual technique and the stationary phase method gives an explicit physically visual representation for the guided waves excited contactlessly in the composite plate. Utilizing this framework, the optimal transducer tilt angles for exciting waves of the desired type at specific center frequencies are determined. Numerical results demonstrating the dependence of the amplitude–frequency characteristics of the excited waves and the optimal transducer tilt angle on the sample’s structure and elastic properties are presented.</p>