The complete elastic constant tensor, i.e. the real and imaginary parts C ijkl and Q i j k l − 1 , of icosahedral AlPdMn quasicrystal were measured at megahertz frequencies, from 4 K to room temperature, using electromagnetic acoustic resonance. The temperature dependence of C ijkl was analyzed using an Einstein oscillator model and a quasiharmonic approximation. The overall mode Grüneisen parameter γ is 2.0, in agreement with a previous thermal expansion measurement. Internal friction Q i j k l − 1 behaved normally throughout the measured temperature range. These results suggest that the lattice anharmonicity of i-AlPdMn is similar to usual crystalline materials despite its significant difference in structure.