The change of resistance in uniaxial tension was measured for several single-crystal specimens of p-type InSb over the range 77°K to 350°K. The difference between the donor and acceptor concentrations for these specimens ranges from 3×1015 cm-3 to 7×1017 cm-3. The piezoresistance coefficients were found to depend on impurity concentration. The elasto-Hall constant was measured at 77°K for the purest specimens and the experimental results indicate that, in the extrinsic range, the large piezoresistance is primarily due to stress induced changes in the tensor mobility of the holes. The shear coefficients were found to vary approximately linearly with T-1 in the extrinsic range. It is concluded that the valence band extrema occur at, or very near, K=0 in the Brillouin zone with energy surfaces similar to those of Si and Ge.