Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. When the guiding structure is embedded into a solid matrix, waveguides are open and waves can be trapped or leaky. With numerical methods, one of the difficulty is that leaky modes attenuate along the axis (complex wavenumber) and exponentially grow along the transverse direction. The goal of this work is to propose a numerical approach for computing modes in open elastic waveguides combining the so-called semi-analytical finite element method (SAFE) and a perfectly matched layer (PML) technique.