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First-principles calculations are performed to study pressure effects on structure, magnetic and mechanical properties of FexB (x=1, 2, 3) compounds using density functional theory (DFT) within GGA approximation. The three structures are studied in the pressure range from 0 to 90 GPa, in order to predict the critical transition pressure from magnetic to nonmagnetic states (NM) and a possibility of superconductivity in this state was predicted. Mechanical anisotropies in both cases are discussed by calculating different anisotropic indexes and factors. We have plotted the three dimensional (3D) surfaces and planar contours of bulk and Young moduli of FexB (x=1, 2, 3) compounds at several crystallographic planes, ((100), (010) and (001)) to reveal their elastic anisotropy. Furthermore, the relationship between crystal structure and material hardness of FexB is also investigated by calculating hardness of Fe-B and B-B bonds using Mulikan population analysis and semi empirical hardness theory. By the elastic stability criteria, it is predicted that FexB are stable up to the selected pressures.