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In multilayer microwave integrated circuits such as low-temperature co-fired ceramics or multilayered printed circuit boards, waveguide-like structures can be fabricated by using periodic metallic via-holes referred to as substrate integrated waveguide (SIW). Such SIW structures can largely preserve the advantages of conventional rectangular waveguides such as high-Q factor and high power capacity. However, they are subject to leakage due to periodic gaps, which potentially results in wave attenuation. Therefore, such a guided-wave modeling problem becomes a very complicated complex eigenvalue problem. Since the SIW are bilaterally unbounded, absorbing boundary conditions should be deployed in numerical algorithms. This often leads to a difficult complex root-extracting problem of a transcend equation. In this paper, we present a novel finite-difference frequency-domain algorithm with a perfectly matched layer and Floquet's theorem for the analysis of SIW guided-wave problems. In this scheme, the problem is converted into a generalized matrix eigenvalue problem and finally transformed to a standard matrix eigenvalue problem that can be solved with efficient subroutines available. This approach has been validated by experiment.