The present work aims to investigate the structural parameters, elastic constants and thermodynamic properties of scandium mono-phosphide (ScP) binary compound. We employed the Quantum Espresso code with the projected augmented wave (PAW) pseudopotentials approach in the framework of the density functional theory (DFT). Firstly, we report the ground state parameters of both NaCl-type (B1) and CsCltype (B2) phases. Generally, our obtained data agree well with other results of the literature. Our calculated value (<$E5,205~roman A back 45 up 35 symbol Р>) of <$Ealpha sub 0> for B1 phase deviates from the experimental result (<$E5,312~roman A back 45 up 35 symbol Р>) by around 2 %. The structural phase transition from B1 to B2 phase under pressure was determined. Our calculation shows that ScP transforms from B1 to B2 phase at a pressure of 108 GPa, with a volume collapse of 4,3 %. Secondly, we calculate the elastic stiffness constants, elastic moduli, anisotropy factor, Poisson's ratio, Vickers hardness, fracture toughness, acoustic wave speeds, Debye temperature and melting point of the most stable phase (B1). Our data of the elastic constants are also in good agreement with other theoretical results of the literature. The Vickers hardness HV of ScP compound was found equal to 12,7 GPa, while the Debye temperature <$Etheta sub D> was found at around 551,8 (522,1) K. Moreover, some interesting thermodynamic properties, especially the energy, free energy, entropy and constant volume heat capacity as a function of temperature were also reported and discussed.

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