An effective dipole potential is used to calculate the elastic and piezoelectric coefficients for a static-lattice model of tetragonal HCN, using the generalized thermodynamic theory of internal strain. The model is unstable with respect to molecular rotation away from the tetragonal axis, owing to the use of a point effective dipole. An improved potential would represent the molecule as a set of polarizable point dipoles. Isotropic pressures makes HCN expand along the tetragonal axis as it contracts perpendicular to the axis, because of strong elastic cross-linking. The piezoelectric stress coefficient for shear strain is dominated by the contribution from molecular rotation. Both physical and thermodynamic coefficients are calculated; the differences between the coefficients, which arise from the permanent polarization in HCN, are especially marked in the strain coefficient.