We have studied the exciton absorption of single-crystalline ZnTe epilayers grown by metalorganic vapour-phase epitaxy on (001) GaAs substrates. More than 1-mu-m of the 2-mu-m thick layers, including a dislocation-rich interface region, has been removed by a chemical etching procedure. Transmission and reflectivity measurements have been performed on the same samples with thicknesses below 1-mu-m. Samples glued on a glass substrate reveal two exciton absorption structures, which are identified to be the n = 1 heavy- and light-hole excitons. This splitting nearly disappears for free-standing layers. The absorption maximum appears at the transverse exciton energy, which has been determined by a polariton model for the reflectivity. The deformation potentials obtained from hydrostatic pressure measurements and from the shift and splitting of the exciton are a = -5.5 eV and b = -1.4 eV at low temperatures.