The Gru¨neisen parameter has been defined as the pressure response in a material to a change in internal energy with the strains held constant. The Gru¨neisen parameter does not account for the oriented response of anisotropic materials; the Gru¨neisen tensor is developed to account for this response. The Gru¨neisen tensor is stated explicitly for several crystal classes. Alpha‐quartz is considered as an example of an anisotropic material, and specific values for its Gru¨neisen tensor are presented.