The finite element model describing the change of the stress-strain state of the sclera (the outer shell of an eye) loaded by an impression-type tonometer - the Schiøtz tonometer is presented. The simulation is performed with the software package ANSYS, Inc. The elastic system cornea-sclera is modeled as two thin transversely isotropic adjoint spherical shells with different radii of curvature and biomechanical properties loaded by the internal pressure and two loads with concave bases (footplate and plunger). The effect of the weight of the plunger and the thickness of the cornea on the tonometric pressure readings obtained due to the standard method of data processing for Schiøtz tonometry is studied. The obtained values are compared with the values found from the condition of constant internal volume of the deformed composite shell.