Abstract Oceanic intraseasonal Kelvin waves (KWs) help modulate upper-ocean thermal characteristics, providing feedbacks to important coupled air-sea phenomena in the tropics. The recent availability of daily thermocline depth fields from several CMIP6 models makes it possible to evaluate the performance of KWs and identify potential sources of bias. Most models fail to simulate a realistic spatial distribution of KW variability. Models simulate large variability of KWs in the western or eastern Pacific rather than in the central Pacific as observed. The modeled KWs propagate slowly (about 1.5 m/s) compared to observations (about 2.5 m/s). This slow propagation is also identified in wavenumber-frequency spectra for KWs and meridional KW structures, which is more consistent with a second baroclinic mode structure in models compared to the first baroclinic mode structure in observations. An analysis of the relative contributions of vertical wavenumber and background ocean stability to KW phase speeds indicates that the high vertical wavenumber bias in models contributes most to the slow propagation, in which the higher-than-observed vertical wavenumbers implying the biased incorporation of higher baroclinic modes in model KW structure. This finding is further supported by the results of vertical mode decomposition that incorporates background density profiles. These results indicate that a realistic representation of the KW vertical structure is essential to produce realistic KW propagations in models.