Abstract: Classical perfectly matched layer (PML) absorbing boundary is certified an efficient method to suppress spurious edge reflections in seismic modeling. However, when modeling Rayleigh waves with the existence of free surface, the classical PML algorithm may become unstable in the case that Poisson’s ratio of the medium is high. On the basis of defects of classical PML, such as its inherent instability and the effects of grazing incidence, multiaxial perfectly matched layer, convolutional perfectly matched layer and multiaxial convolutional perfectly matched layer are developed. Six implementations of planar free-surface boundary conditions and principles of four perfectly matched layer methods are introduced, and forward modeling of 2D half-infinite model using staggered grid finite-difference method are given to study the stability of different methods. Through the comparison of waveform between numerical solution and analytical solution, we can illustrate the accuracy and applicability of these methods in this paper. The results show that Poisson’s ratio and implementations of planar free-surface have an important influence on the effects and stability of wavefield simulation.