In linear elasticity, the Lamé parameters are the two parameters

  • λ, also called Lamé's first parameter.
  • μ, the shear modulus or Lamé's second parameter. Also denoted $ G $.

which in homogenous, isotropic materials satisfy Hooke's law in 3D,

$ \sigma=2\mu \varepsilon +\lambda \; \mathrm{tr}(\varepsilon)I $

where σ is the stress, ε the strain tensor, the $ \scriptstyle I $ the identity matrix and $ \scriptstyle\mathrm{tr}(\cdot) $ the trace function.

The first parameter λ has no physical interpretation, but it serves to simplify the stiffness matrix in Hooke's law. The two parameters together constitute a parametrization of the elastic moduli for homogeneous isotropic media, and are thus related to the other elastic moduli.

The parameters are named after Gabriel Lamé.


  • F. Kang, S. Zhong-Ci, Mathematical Theory of Elastic Structures, Springer New York, ISBN 0-387-51326-4, (1981)
  • G. Mavko, T. Mukerji, J. Dvorkin, The Rock Physics Handbook, Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)

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