In this paper, we investigated the structural, electronic, elastic, and optical properties of the chalcopyrite structure CdSiP2 under pressure from first principles in the frame of the density functional theory (DFT). It is found that the obtained lattice constants of CdSiP2 under zero pressure and zero temperature from our calculations are in favorable agreement with the available experimental data and other theoretical ones. The pressure dependences of the elastic constants Cij; bulk modulus B; shear modulus G; elastic anisotropy index AU, AB, and AG; and Young’s modulus E of CdSiP2 are also successfully obtained for the first time. Especially, the elastic constants Cij and the Young’s modulus E under high pressure up to 20 GPa are obtained and analyzed systematically for the first time. In addition, our calculations give a band gap of 1.358 eV, indicating that the chalcopyrite structure CdSiP2 is a semiconductor, consistent with other theoretical results. Finally, the optical properties such as the dielectric function, refractive index, absorption coefficient, and extinction coefficient for energy up to 22.5 eV under pressure have also been reported.