A Hyperelastic material model of vulcanised rubber compounds, defined as a strain energy function, is used to describe its mechanical behaviour. The relation of strain energy function to stress, following the study of Yeoh, was employed. The simplest relation of the reduced true stress for uniaxial tension or uniaxial compression (O-t r) and for simple shear (Tr) is used as the following cubic function in (I1-3) : O-tr or Tr = 2C10 + 4C20 (I1-3) + 6C30 (I1-3)2 where I1 is the first invariant and C10, C20 and C30 are constants, which are determined from those simple tests. Three vulcanised SBR compounds and one vulcanised NR compound were examined on those three simple deformation modes. An agreement of the experimental stress-strain relation to finite element analysis, using COSMOS/M was found for the four compounds tested in compression and simple shear modes. This agreement was also confirmed with other three NR compounds, tested in compression and simple shear modes. However, discrepancy was clearly observed in the case of high carbon-black loaded SBR compounds tested in tension mode.