Surface waves are increasingly attractive for ultrasonic NDE of high technology materials. In previous works, the characterization of viscoelastic and metallic plates has been carried out when geometrical laws of acoustics apply. It has been seen that the accuracy of a material characterization depends strongly on the redundancy of the information of the ultrasonic beam in this material. Good accuracy can be achieved if multiple pulses propagate through the plates. This conclusion may be very useful if one tries to characterize a material when non-geometrical laws of acoustics take place giving birth to leaky surface waves propagation. The aim of this work is to study the different possible generated surface leaky waves in materials. These waves are used for retrieving the acoustic parameters of the device under test. A theoretical model based on the complex harmonic waves combination is used. This model has already been developed for material characterization under normal conditions and is extended here to cover the description of the non-specular effects. The acoustic properties of the material are retrieved by inversion based on applying a consistent estimator on the experimental measurements and the developed model.