Abstract: Artificial boundaries are imposed on the vertical boundaries between exterior semi-infinite layered element zones and interior finite element zone. After deducing the semi-infinite layered element stiffness matrix, the dynamic equation of boundary nodes is obtained and is transformed into an eigenvalue problem with given excitation frequency. Eigenvalues and corresponding eigenvectors are obtained by solving the eigenvalue formulation. Boundary matrixes, embodying right-left exterior infinite media’s effect on the interior finite element zone, are obtained by mode superposition principle, viz. the consistent boundary condition. Boundary matrixes are assembled with the stiffness matrix of interior finite element to simulate P-wave propagation into in-plane infinite media. Numerical example demonstrates the accuracy and reliability of the consistent boundary.