A waveguide-based surface plasmon resonance (SPR) sensor with an adsorbed layer is analyzed using the beam-propagation method. For two-dimensional (2-D) models, numerical results show that the change in thickness of the adsorbed layer placed on the metal leads to a significant shift of the maximum absorption wavelength. Through eigenmode analysis, the maximum absorption wavelength is found to be consistent with the cutoff wavelength of the second-order surface plasmon mode. The designed 2-D sensor shows an absorption wavelength shift from 0.595 to 0.603 µm, when the analyte refractive index is increased from 1.330 to 1.334. After a basic investigation using the 2-D models, we next study 3-D models. When the metal with the absorbed layer is wide enough to cover the core region, the 3-D results are similar to the 2-D results. However, as the metal width is reduced, the absorption wavelength shifts toward a shorter wavelength and the sensitivity to the refractive index change degrades gradually. The degradation of the sensitivity is considerable when the metal width is narrower than the core width. As a result, the metal width of the practical SPR sensor should be slightly wider than the core width so as to maintain the sensitivity corresponding to that obtained for the 2-D model.