The aim of this article is to evaluate the axial stress of a thin cylindrical rubber specimen bonded between two steel cylindrical plates. The thickness of the rubber with respect to its diameter is small. It was assumed that the rubber is described by a Neo-Hookean strain energy function. A theoretical equation was developed to correlate the diametral contraction eta with respect to strain epsilon within the sample. The equilibrium equations of motion and the incompressibility constraint with the free stress condition of R = A mere used to determined the axial stress stale.