Full Heuslers alloys are a fascinating class of materials leading to many technological applications. These have been studied widely under ambient conditions. However, less attention been paid to study them under the effect of compression and strain. Here in this work Co2YZ (Y= Cr, Nb, Ta, V and Z = Al, Ga) Heusler alloys have been studied comprehensively under pressure variations. Calculated lattice constants are in reasonable agreement with the available data. It is determined that lattice constant deceases with the increase in tensile stress and increases by increasing pressure in reverse direction. Band profiles reveals the half metallic nature of the studied compounds. The bond length decreases while band gap increases in compressive strain. The compounds are found to be reflective in visible region, as characteristics of the metals. The magnetic moments reveal the half-mettalic ferromagnetic nature of the compounds.