In order to solve the wave scattering problems due to irregular topography, a hybrid method based on the variation of a modified functional was developed. Introducing finite elements to mesh the irregular region, and the series functions as the scattering waves, the matrix equation could be obtained numerically. By using the sets of transfinite interpolation function, coordinates and nodal numbers of the finite region including an irregular region were determined in a simple way. As the anti-plane Lamb’s series were used, the anti-plane scattering problems due to a single topography, such an oblique truncated canyon, a partially filled alluvial valley, a circular-arc layered alluvial valley, and a dike, were solved. For the anti-plane scattering problems due to a complex surface topography, such as two canyons, a semi-circular hill and a semi-circular canyon, as well as a semi-circular hill and a semi-circular alluvial valley, were solved completely. In addition, a complex topography including a surface canyon with an underground cavity, the irregularity region meshed via arithmetic progression, the formula of the internal division point, and the transfinite interpolation function, made the hybrid method extend the solving this problem. On the other hand, a Lamb’s series satisfied the layered medium in the anti-plane condition was introduced to solve the scattering problem due to an alluvial valley embedded on the layered half-space. It showed the power of hybrid method in solving the anti-plane scattering problems. Furthermore. A Lamb’s series satisfied the in-plane problem was also introduced to solve the scattering problem of canyon due to P waves. In the last decade, we extend the proposed hybrid method to solve various scattering problems by introducing the transfinite interpolation function with the Lamb’s series. The scattering problems due to different complex topographies will be discussed in the future work.