A linear, periodic model using the long-wave approximation on the equatorial β-plane is forced by the annual cycle of zonal wind stress from the Pacific Ocean. The forcing is deduced from the monthly data set of Hellerman and Rosenstein. The model results are compared with observations of the annual cycle which are mainly of temperature in the upper central Pacific Ocean from the Hawaii-Tahiti shuttle experiment. The agreement is good in phase, but poor in amplitude. The effect on model results of different friction assumptions and coefficients shows that no tuning of the parameters significantly improves the comparison with observations. The model is also used to study the effects of the forcing function, a sharp thermocline and friction which are all very important in determining the energy distribution below the thermocline. It is shown that beams occur only in the unphysical situation of inviscid flow with simple forms for the forcing function. The poor comparison with observations is used to draw conclusions about the shortcomings of present linear, equatorial models. They are: the buoyancy frequency can only be a function of depth, and the friction assumptions, which keep the vertical modes independent, have unrealistic profiles with depth and do not give realistic amplitudes both in the upper ocean and below the thermocline.