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Wave propagation phenomena in unbounded domains occur in many engineering applications, e.g., soil structure interactions. The considered problem is often modeled by the theory of elasticity which is in some applications a sufficient accurate approximation. Nevertheless, the interaction of the solid- and the fluid phase attribute a time dependent character to the mechanical response of the saturated soil, which can be modeled by Biot‘s theory of poroelasticity. When simulating unbounded domains, infinite elements are a possible choice to describe the far field behavior, whereas the near field is described through conventional finite elements. Hence, an infinite element is presented to treat wave propagation problems in unbounded elastic and saturated porous media. Infinite elements are based on special shape functions to approximate the semi-infinite geometry as well as the Sommerfeld radiation condition, i.e., the waves decay with distance and are not reflected at infinity. To provide the wave information the infinite elements are formulated in Laplace domain. The time domain solution is obtained by using the convolution quadrature method as inverse Laplace transformation. The temporal behavior of the near field is calculated using a standard time integration scheme, i.e., the Newmark-method. Finally, the near- and far field are combined using a substructure technique in any time step. The accuracy as well as the necessity of the proposed infinite elements, when unbounded domains are considered, is demonstrated with different examples.