Cavitation free energy Delta G(cav) corresponding to the formation of an excluded volume cavity in water, is calculated for a large set of organic molecules employing the thermodynamic integration procedure, which is realized as the original two-step algorithm for growing the interaction potential between the hard cavity wall and the water molecules. A large variety of solute systems is considered. Their characteristic radii change in the range 3-7 angstrom; spherical cavities with radii 3-6 angstrom are also studied. The interaction between water molecules is described by the four-site nonpolarizable TIP41 model. The diversity of the trial molecular set is provided by using a specially formulated nonspherical criterion classifying the cavity shapes according to their deviation from a sphere. Molecular objects were partly taken from the data base NCI Diversity with the aid of this criterion. The so-computed free energies are approximated by the linear volume dependence Delta G(cav)(V) = xi V, where V is the cavity volume. This relation works fairly well until the cavity size becomes very large (the effective radius larger than 7 angstrom). The volume dependence valid for solutes of arbitrary shapes can be included in a calculation of the nonpolar free energy component as required in the implicit water model.