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 form W=G4∑i=13(λi−1λi)2+H4∑t=13(λ2i−1λ2i), where the λi's are the principal stretches (1+principal extension), G is the modulus of rigidity, and H is a new elastic constant not found in previous theories. The differences between the principal stresses are σi[minus]σi=λi∂ W/∂λi[minus]λi∂ W/∂λi.

Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.