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Attempts at the mechanical identification of the human eyeball are often not very effective for two reasons: the material parameters determined by tension tests on corneal and scleral tissue specimens are not sufficiently accurate while numerical models of the eye, integrating material and geometric parameters, are often based on unrealistic assumptions. The examples presented here cover refractive surgery, Goldmann applanation tonometry and the optical self-adjustment of the eye. The discussed problems are illustrated with calculations showing that it is possible to effectively use a biomechanical model of the eye to identify its material parameters. Also the handicaps, the Imbert–Fick law among them (numerical calculations do not corroborate this law), lying at the basis of applanation tonometry are demonstrated. The conclusions can help to create a realistic numerical model of the eyeball.