Experimental and theoretical results of the intraband optical Stark effect in bulk CdTe are reported. The intensity-dependent blue shift of the 1s exciton under the influence of a strong CO2 pump laser and its dependence on the polarization of pump field and test field are shown in transmission and reflection measurements. The fine structure of 2P excitons is clearly resolved by two-photon absorption experiments. For the first time the Stark shift of 2P excitons is detected. The theoretical description takes into account the complex valence band structure, which results in a pump-field-induced heavy-light-hole splitting and a susceptibility which depends on the polarization of pump field and test field. Good agreement with experimental results and theoretical predictions is achieved, if an additional intensity-dependent damping and the inhomogeneous field distribution due to multiple reflection in the sample are taken into account.