In practical engineering, plates and pipes are often embedded or immersed in external media such as soil or water. When the dimensions of the surrounding medium significantly exceed those of the central structure, the guided wave propagation characteristics in such open waveguide structures differ markedly from those in free-boundary waveguides. Energy leakage into the external medium introduces axially attenuated leaky modes, which severely limit the effective propagation distance of guided waves in practical inspection scenarios[1]. Thus, accurately characterizing the propagation properties of leaky modes is essential for guided wave-based detection in open waveguide systems. This study presents recent progress in the computation of leaky modes in open waveguides based on the semi-analytical finite element method combined with perfectly matched layers (SAFE–PML). As leaky modes attenuate along the propagation direction while exhibiting exponential growth in the transverse direction, the PML technique is introduced in the transverse direction within the SAFE framework to artificially attenuate these exponentially increasing fields. Hence, an effectively unbounded medium can be modelled using a finite thickness. This approach enables accurate modeling of complex central waveguide structures while significantly reducing the computational cost associated with the surrounding medium. Numerical modeling has been completed for both the plate and pipe structures embedded in an infinite solid or immersed in an infinite liquid. The accuracy of the proposed method has been validated through comparisons with results obtained using the commercial software Disperse. In addition, with the newly introduced function of open waveguide, the software SAFEDC has been upgraded to Version 2.0. This new version incorporates modules for plate structures and pipe structures embedded in infinite solids, and pipe structures immersed in infinite liquids. Users can define material properties and geometric parameters of plate and pipe structures. Finally, the dispersion curves are plotted and can be saved for further analysis.