A theoretical technique for determining the volume dependence of the thermal expansion coefficient &agr; along an isotherm is developed for solids which exhibit a linearUs‐up(i.e., shock velocity‐particle velocity) relationship. The method is founded on an accurate Gru¨neisen equation of state utilizing the temperature‐independent Gru¨neisen parameter &ggr; which has been calculated from experimental shock data. Detailed results are presented for several isotherms at pressures as high as 1 Mbar. Based on the accuracy of the Gru¨neisen parameter, the accuracy of the calculated thermal coefficient &agr; is estimated to be within ±10% down to 20% compression with greater accuracy for lower compressions.