This thesis is motivated by a project with an industry partner. The first part of the thesis covers this project. The main topic is the inspection of the pipe weld quality for butt fused polymer pipes made out of PP and PVDF. The special requirements of the project partner include a non-contact and non-destructive testing method that can be applied from the outside of the pipes. To meet these specifications, an air coupled ultrasonic inspection setup using Lamb waves is developed to examine the pipe weld bead and improve the reliability of the welding process. With such a system, expensive destructive testing methods can be avoided and the leakage of piping systems due to flawed weldings can be prevented. The goal of the project is to find defects in the pipe weld with a size down to 20% of the pipe wall thickness. With the chosen method, defects in the pipe weld create a w-shaped pattern in the time domain signal amplitude and defects with a size of 50% of the wall thickness are detected. The pipes feature material inhomogeneities, a varying weld bead shape and changes in the pipe geometry that are well within the tolerances and therefore are not considered defects. But these effects influence the evaluated signal in the same order of magnitude as the defects, limiting the overall performance of the inspection method. In the second part of this thesis, the air coupled examination process of thin walled polymer specimens is studied in depth, in particular the underlaying physical effects. The challenges are approached by simplifying the problem. First, the welded pipes are replaced by pipes without weld that are examined with an additional reference measurement of the undamaged part of the pipes. In a next step, the pipe geometry is abandoned completely and instead PMMA plates are used as specimens. The goal is to detect defects inside plates with a size comparable to the wavelength and to increase the robustness of the method to small variations in the specimen geometry and material. The challenges are the complex signals generated and acquired with air coupled transducers. This includes different Lamb modes that may overlap in time, direct pressure waves from the transmitter to the receiver and the low signal to noise ratio as well as the evaluation of the dispersive Lamb waves. In addition to the experiments that are carried out, an idealized two-dimensional numerical model is introduced. With these simplifications, the basic physical effects are investigated separately. This includes the excitation of the different Lamb modes inside the plate with air coupled transducers and its dependence on the transmitter angle. Also the detection of the pressure waves reradiated by the propagating Lamb waves is examined. And finally, the interaction of Lamb waves with defects, especially Lamb mode conversion, is studied. In parallel, signal analysis algorithms are developed that can handle dispersive Lamb wave signals. With the help of the simplified setup using plates, four key parameters are identified. These parameters are the two transducers angles as well as two distances. The transducer to specimen surface distance needs to be as small as possible and the transmitter to receiver distance should be as large as possible. The transmitter angle can be tuned to excite an almost pure A0 Lamb wave. The S0 Lamb waves can not be excited in a pure fashion, but are always excited together with A0 Lamb waves of lower magnitude. Multiple reflections of the pressure waves occur between transmitter, specimen surface and receiver. This behavior depends heavily on the specific setup geometry. At each impact of the pressure wave on the specimen surface, Lamb waves are excited and the exact composition of the Lamb modes di ffers each time. The receiver angle can be tuned to one specific Lamb wave phase velocity (and therefore Lamb mode), all others are detected with lower amplitude. Two signal analysis algorithms are developed that allow to split the signal into the individual Lamb modes, a data driven method and a model based one. Both algorithms also help to remove noise from the signal. The model based algorithm also gives an estimation on the plate thickness and material properties. Both methods rely on multiple measurements of the waves along their propagation path. Finally, the Lamb mode conversion method is successfully applied for the examination of plates with defects. With the help of the signal analysis algorithms, Lamb mode conversion can be shown and the defect signal can be isolated from all other effects, making the method more robust to changes in the plate thick- ness. Additionally, the defects can also be located. The evaluation based on the time domain signal amplitude of Lamb waves acquired by air coupled transducers is very sensitive to the variation of the specimen geometry and material inhomogeneities. Lamb mode conversion at symmetry breaking defects can be exploited for defect detection. This method requires algorithms that can handle dispersive Lamb waves and are capable of separating the individual Lamb modes. This also makes multiple measurements along the propagation path necessary. Both signal analysis methods also reduce the noise significantly. The new method is suited for defect detection and also localization and more robust to small variations of the specimen. It is interesting not only for the application in the area of pipe weld inspection, but also for other materials as composites.