Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. However, guiding structures are often buried in a large domain, considered as unbounded. Waveguides are then open and waves can be trapped or leaky. Analytical tools have been developed to model open solid waveguides but these tools are limited for simple geometries (plates, cylinders). With numerical methods, a difficulty is due to the unbounded geometry. Another issue is due to the presence of leaky modes, which grow exponentially along the transverse directions. The goal of this work is to implement a numerical approach to calculate modes in three dimensional elastic open waveguides, which combines the semi-analytical finite element method and the perfectly matched layers (PML) technique. Both Cartesian and cylindrical PML are implemented.