In this work, structural, electronic, magnetic, thermal and mechanical properties of Mn2ZrZ (Z= Ge and Si) under pressure upto 50 GPa is studied using state of the art density functional theory. In structural properties, under pressure ground state optimizations are performed to check the thermodynamic stability of studied alloys. Furthermore, enthalpy of formation and elastic stability criteria affirms the thermodynamic stability in studied alloys. Pugh ratio suggests that, Mn2ZrGe and Mn2ZrSi remain ductile and brittle in nature, respectively throughout pressure upto 50 GPa. Moreover, large elastic anisotropic response is observed for both alloys. In electronic properties density of states and band gaps are discussed in detail which affirms the ferromagnetic half metallic nature of alloys. Our computed results, such as optimized ground state lattice constant, band-gap and magnetic moment are consistent and have matched excellently with available literature at ambient conditions. In mechanical properties, Debye temperature factor, minimum thermal conductivity and melting temperature is observed to increase with pressure while, Grüneisen anharmonicity factor decreases. However, to date, there are no reports available in literature with under pressure results upto 50 GPa. Therefore, this work illustrates new findings of Mn2ZrZ under pressure for potential applications in thermal actuators and spintronic devices.