Abstract Output from 20 coupled global climate models is analyzed to determine whether convectively coupled Kelvin waves exist in the models, and, if so, how their horizontal and vertical structures compare to observations. Model data are obtained from the World Climate Research Program’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset. Ten of the 20 models contain spectral peaks in precipitation in the Kelvin wave band, and, of these 10, only 5 contain wave activity distributions and three-dimensional wave structures that resemble the observations. Thus, the majority (75%) of the global climate models surveyed do not accurately represent convectively coupled Kelvin waves, one of the primary sources of submonthly zonally propagating variability in the tropics. The primary feature common to the five successful models is the convective parameterization. Three of the five models use the Tiedtke–Nordeng convective scheme, while the other two utilize the Pan and Randall scheme. The 15 models with less success at generating Kelvin waves predominantly contain convective schemes that are based on the concept of convective adjustment, although it appears that those schemes can be improved by the addition of convective “trigger” functions. Three-dimensional Kelvin wave structures in the five successful models resemble observations to a large degree, with vertically tilted temperature, specific humidity, and zonal wind anomalies. However, no model completely captures the observed signal, with most of the models being deficient in lower-tropospheric temperature and humidity signals near the location of maximum precipitation. These results suggest the need for improvements in the representations of shallow convection and convective downdrafts in global models.