Whereas the 1st Piola–Kirchhoff stress relates forces in the current configuration to areas in the reference configuration, the 2nd Piola–Kirchhoff stress tensor <math>\boldsymbol{S}</math> relates forces in the reference configuration to areas in the reference configuration. The force in the reference configuration is obtained via a mapping that preserves the relative relationship between the force direction and the area normal in the current configuration.
:<math>
 \boldsymbol{S} = J~\boldsymbol{F}^{-1}\cdot\boldsymbol{\sigma}\cdot\boldsymbol{F}^{-T} ~.
</math>

In [[index notation]] with respect to an orthonormal basis,
:<math>S_{IL}=J~F^{-1}_{Ik}~F^{-1}_{Lm}~\sigma_{km} = J~\cfrac{\partial X_I}{\partial x_k}~\cfrac{\partial X_L}{\partial x_m}~\sigma_{km} \!\,\!</math>

This tensor is symmetric.

If the material rotates without a change in stress state (rigid rotation), the components of the 2nd Piola–Kirchhoff stress tensor remain constant, irrespective of material orientation.

The 2nd Piola–Kirchhoff stress tensor is energy conjugate to the [[Finite strain theory#Finite strain tensors|Green–Lagrange finite strain tensor]].

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If we pull back <math>d\mathbf{f}</math> to the reference configuration, we have
:<math>
  d\mathbf{f}_0 = \boldsymbol{F}^{-1}\cdot d\mathbf{f}
</math>
or, 
:<math>
  d\mathbf{f}_0 = \boldsymbol{F}^{-1}\cdot \boldsymbol{N}^T\cdot\mathbf{n}_0~d\Gamma_0
         = \boldsymbol{F}^{-1}\cdot \mathbf{t}_0~d\Gamma_0
</math>

The PK2 stress (<math>\boldsymbol{S}</math>) is symmetric and is defined via the relation
:<math>
  d\mathbf{f}_0 = \boldsymbol{S}^T\cdot\mathbf{n}_0~d\Gamma_0 = \boldsymbol{F}^{-1}\cdot \mathbf{t}_0~d\Gamma_0
</math>
Therefore,
:<math>
  \boldsymbol{S}^T\cdot\mathbf{n}_0 = \boldsymbol{F}^{-1}\cdot\mathbf{t}_0
</math>