The electronic structural and mechanical properties of III-V Gallium Phosphide (GaP) nano-crystals zinc-blende stable (ZB) phase under pressure dependence have been studied via the model of the density functional theory (DFT) in combination with the large unit cell (LUC) approach at (8, 16, 54 & 64) atoms. The exchanges and correlations (XC) energy has been defined in all approaches through generalized gradient approximations of the Perdew-Burke-Ernzerhof (GGA-PBE), and determination of GaP characteristics in the case where the pressure has been increased from 0GPa to ±50GPa. Elastic parameters like elastic constants (C11, C12 & C44), Kleinmann parameter (ξ), Zener anisotropic factor (A), shear modulus (G), Young's modulus (E), Poisson’s ratio (v), Bulk modules (B) of GaP-ZB structure have been calculated and showed systematic variation with a pressure increase. Our calculations show that Bulk modules and sound speed increase with an increase in the number of core atoms. In this systematic approach, it has been found that the B/G ratio is 1.58 for this compound and it exhibits a negative Cauchy pressure, classifying GaP as brittle. The results were discovered to be consistent with other theoretical as well as experimental results. The present study directly relates to the latest experimental works on the III-phosphide compounds. The current results provide information and direction for further investigation into the fundamentals and potential applications of gallium phosphate (GaP) nanocrystals. In addition, we attempted to compare the results of the investigation with some similar types of compounds that are already documented in the literature. We believe that our study will have a significant impact on both the field of research and contemporary technology based on semi-conducting materials.