We reported for the first time a theoretical study of structural, electronic, optical, elastic and thermodynamic properties of Ca4SiN4 and Ca4GeN4, based on DFT + PP-PW approach. The calculated structural parameters are in good agreement with the experimental data. Both considered alkaline earth metalloid nitrides are more compressible along the c-axis. The band structure calculations showed that the studied compounds are direct bandgap (Γ¬Γ) semiconductors; the energy bandgap given by GGA (LDA) is equal to 1.501 (1.598) eV and 1.462 (1.583) eV for Ca4SiN4 and Ca4GeN4, respectively. The optical parameters including dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity and electron energy-loss function were computed for different polarizations of the incident light. Single-crystal elastic constants, polycrystal elastic moduli and their pressure dependence were calculated and discussed. The two nitrides satisfy the mechanical stability criteria over the considered pressure range. We have also investigated their thermodynamic properties by computing Debye temperature, thermal expansion coefficient α and heat capacities CP and CV.