Experimental and numerical results are presented on the behavior of guided waves in elastic plates in plane strain that include a Gaussian variation of their section, located between two areas of constant thickness. The area of varying section is wide compared to the used wavelengths, which allows wave propagation inside this area. The experimental results show that an incident Lamb wave is indeed converted into an adiabatic wave inside the varying section domain. A trapped wave in the Gaussian domain is also observed, depending on the incident mode and on the Gaussian maximum height. Outside the varying section domain, conversion into different Lamb waves is observed. This conversion phenomenon is experimentally quantified by the measurement of the Lamb wave normal displacement and of its carried energy. A numerical study, based on the Finite Elements Method is performed, and successfully compared to the experimental results.