It is postulated that (A) the material is isotropic, (B) the volume change and hysteresis are negligible, and (C) the shear is proportional to the traction in simple shear in a plane previously deformed, if at all, only by uniform dilatation or contraction. It is deduced that the general strain‐energy function,W, has the formW=G4i=13&lgr;i−1&lgr;i2+H4t=13&lgr;i2−1&lgr;i2,where the &lgr;i's are the principal stretches (1+principal extension),Gis the modulus of rigidity, andHis a new elastic constant not found in previous theories. The differences between the principal stresses are &sgr;i[minus]&sgr;i=&lgr;i∂W/∂&lgr;i[minus]&lgr;i∂W/∂&lgr;i.Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.