Laser ablation of human and rabbit corneas has been studied at 211 and 263 nm with 25 ps pulses. The pulses are obtained from the 4th and 5th harmonics of the output of a Nd:YLF laser system. This system provides laser pulses with maximum pulse energy of 25 (mu) J at 211 nm and 31 (mu) J at 263 nm simultaneously on a cornea at a repetition rate of 1 kHz. The linear incisions and morphology of the collateral tissue damage have been examined by electron microscopy. The dependence of the etch rate on laser fluence has been measured at both of wavelengths. The ablation threshold for human cornea is determined to be 3.0+/- 0.6mJ/cm2 at 211 nm while the thresholds for rabbit cornea are 2.3+/- 0.5mJ/cm2 at 211 nm and 8.0+/- 2mJ/cm2 at 263 nm. We compare these results with the existing data on the corneal ablation by nanosecond UV pulses and discuss the deficiency of the photochemical model. A model of plasma ablation assisted by chromophore absorption has been proposed to interpret the experimental results.