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Tilted-coil antennas (TCAs) have been proposed to increase the directional sensitivity and anisotropy sensitivity of well-logging tools used in oilfield exploration. In this paper, we simulate TCAs in 3-D cylindrically layered and anisotropic earth formations with multiple horizontal beds using an extended numerical mode-matching (NMM) approach. The field components are expanded in terms of longitudinal (vertical) eigenmodes to facilitate the analysis of transverse electric and transverse magnetic fields, which are coupled in this case. The perfectly matched layer is incorporated into the NMM formulation to mimic the Sommerfeld radiation condition in the longitudinal (vertical) direction. NMM results are compared with 3-D simulation results using finite-difference time-domain method and a pseudoanalytical approach based on Sommerfeld integrals (for problems where the latter is applicable), showing very good agreement.