Using the generalized-gradient approximation (GGA) based on density functional theory, we have reported the structural, mechanical, electronic, and lattice dynamical properties of the intermetallic compounds Pd3X (X = Ti, Zr, Hf) with D0(24) and the L1(2) structures. The elastic constants were predicted using the stress-finite strain technique. We performed numerical estimations of the bulk modulus, shear modulus, Young's modulus, Poisson's ratio anisotropy factor, G/B ratio, and hardness. Our studies have showed that all Pd3X (X = Ti, Zr, Hf) with D0(24) and the L1(2) structures are mechanically stable and relatively hard materials with low compressibility, and they could be considered as ductile systems. Also, the phonon dispersion curves and total and partial density of states were calculated and discussed for Pd3X (X = Ti, Zr, Hf). We finally estimated some thermodynamic properties such as entropy, free energy, and heat capacity at the temperature range 0-1000 K. The calculated phonon frequencies of Pd3X (X = Ti, Zr, Hf) are positive, indicating the dynamical stability of the studied compounds. For the first time, we have performed the numerical estimation of lattice dynamical properties for the compounds and still awaits experimental confirmation. The obtained ground state properties are in good agreement with those of experimental and theoretical studies.