Cu₂ZnSnS₄ (CZTS) and Cu₂ZnSnSe₄ (CZTSe) with optimum band gaps about 1.5 eV are important absorbers for solar cells. The elastic constants and the thermo-physical properties of the stannite-type CZTS and CZTSe are calculated by using density-functional theory (DFT) and the quasi-harmonic Debye model. The bonding strength along the [100] and [010] directions is the same to that along the [001] direction and the shear elastic properties of the {001} plane are anisotropic for CZTS and CZTSe. Both compounds exhibit ductile behavior due to their high ratio of bulk modulus to shear modulus (K/G). The values of thermal capacity are close to 200 J/(mol·K) at above 300 K, and the thermal expansion coefficients decrease with increasing pressure at same temperature. The entropy is variable by power-exponent, and the internal energy is almost linear with increasing temperature for CZTS and CZTSe. The Gibbs energy of CZTS is lower than that of CZTSe under same temperature and pressure. The Debye temperatures are 297 and 232 K, and Gruneisen parameters are 2.36 and 2.37 for CZTS and CZTSe at 300 K, respectively.