Density functional theory (DFT) was applied to investigate the structural, electronic, elastic, magnetic, thermodynamic and half-metallic properties of the newly d0 Heusler alloys (HAs) CsCaZ (Z= Ge, Sn and Pb). Spin-polarised calculations show that the compounds studied are half-metallic with a magnetic moment of 1.00 μB at the equilibrium lattice parameter, which obeys the well-known Slater–Pauling rule Mtot = 8 – Zt. The half-metallic behavior of the compounds CsCaGe, CsCaSn and CsCaPb is predicted with respect to the equilibrium lattice constants for CsCaGe, CsCaSn and CsCaPb with a narrow band gap in the majority spin channel. Furthermore, the elastic constants (Cij) showed that these materials are ductile and anisotropic. In addition, the negative values of the calculated formation energy and cohesion energy indicate that CsCaZ (Z= Ge, Sn and Pb) are likely to be experimentally synthesized. Non-equilibrium Gibbs function is employed to calculate the thermodynamic properties through the quasi-harmonic Debye model in which the bulk modulus, heat capacity, Debye temperature, thermal expansion coefficient, and entropy are investigated at 0-20 Gpa pressure and 0-1200 K temperature ranges. The significant half-metallic behavior makes the CsCaZ (Z= Ge, Sn and Pb) compounds strong candidates for spintronic applications.