The energy bands, density of states, charge density, Mulliken population, equation of state and elastic properties of α-CdP2 have been studied. Exchange correlation functional PBEsol is utilized in this study. The optimized equilibrium lattice parameters of the conventional cell have been obtained. The present investigation indicates the existence of an indirect band gap of 1.76 eV in α-CdP2 crystal. Elastic calculations show the mechanical stability of the alpha phase of CdP2 crystal. This work provides an analysis of directional Young’s modulus and linear compressibility for α-CdP2. The study of the elastic anisotropy parameters shows that the alpha phase has a definite elastic anisotropy. The calculated Debye temperature of α-CdP2 is 288.1 K.