The accumulation of helium atoms in metals or metal tritides is known to result in the formation of helium bubbles in the lattice and to cause degradation of the material. Helium is introduced either through neutron transmutation reaction or via the radioactive decay of tritium. We have performed first-principles calculations of interstitial helium inside Pd and Pd tritide using density functional theory (DFT) and the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). We model the growth process of an interstitial helium cluster and find that when the size of the cluster reaches to five atoms, the cluster can induce an energetically favorable vacancy with a self-trapping mechanism. The cluster growth mechanism of interstitial helium is addressed by investigating the associated energetics, cluster configurations, and electronic structural properties. In addition, we study the diffusion properties of helium in palladium-based compounds by performing the nudged elastic band (NEB) calculations. Our computational models propose that by loading the lattice with hydrogen atoms at certain concentration, or substituting with alloying metals can modify the diffusivity by increasing its migration barrier, which may impede the cluster formation in the beginning stage.