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The elastic and thermodynamic properties of TbAl and DyAl under high pressure and temperature are investigated using the density-functional theory (DFT) and the density-functional perturbation theory (DFPT) within the quasi-harmonic approximation (QHA). The calculated lattice and elastic constants at ground state (0 GPa and 0 K) are in agreement with the experimental data and previous theoretical results. Finally, when the pressure is given, all the thermodynamic quantities except for the bulk modulus increase with temperature, but the increase of the thermal expansion coefficient and the heat capacity with temperature becomes smaller. Besides, the effects of pressure on the elastic constants and the thermodynamic quantities are opposite with those of the temperature on them for TbAl and DyAl.