We have studied structural, mechanical and dynamical properties of PdC and CdC compounds to predict the most stable structure. We have focused on seven binary structure types as rock salt (RS), caesium chloride (CsCl), zinc blende (ZB), wurtzite (WZ), tungsten carbide (WC), cadmium telluride (CdTe) and nickel arsenide (NiAs). For modelling exchange-correlation effects we have used generalized gradient (GGA) approximation based on Perdew-Burke-Ernzhorf functional (PBE). The polycrystalline elastic moduli such as Young's and shear moduli, Poisson's ratio, sound velocities, Debye temperatures and shear anisotropic factors have been presented for mechanically stable structures using second-order elastic constants calculated from the stress-strain relations. The results show that PdC is thermodynamically, mechanically and dynamically stable in ZB structure. On the other hand, while CdC is energetically in favor of RS structure, it is mechanically and dynamically stable in ZB structure.