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Abstract: A closed form solution to the second order clasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed normal load, is presented. The method of integral transform is emploved and the case when loading is distributed, in accordance with Hertz's law, is discussed. The limiting solution for mcompressible isotropic clastic material is also derived. Numerical calculattons for the second order clastic material for the displacement and the normal stress in the z-direction are carried out. It is found that, in comparison to the linear elastic case, the displacement increases and the normal stress decreases in the second order clastic matierial.