Abstract: The nonlinear mathematical model is given to describe void nucleation and growth for elastic solid materials. Exact formulae to calculate the critical values of control parameters for cavitation and exact expressions for growth of void radial are derived. For large deformation, finite logarithmic strain measure is used, and the constitutive relationship of materials is basic on Hookean elastic law. The numerical results show that the critical loads of cavitation for Hooke elastic solid in the case of uncompressible materials are slightly lower than the critical loads for uncompressible neo-Hookean hyperelastic materials. The cavity will be suddenly ra-pid growth after void nucleation. This conclusion is agreed with the corresponding conclusion from the damage micromechanics and the theory of cavitated bifurcation for hyperelastic materials. Also, the analysis shows that the loop stress will become infinite when void nucleation. Thus, the materials near the cavity will product plastic deformation if the materials are elastic-plastic. This leads to local failure and fracture of the materials.