Property of matter of the semiconductors quaternary was investigated by the density functional theory and paralleled to the foretelling of the linear elasticity theory. In addition, quaternary alloys of InxGa1-xAs1-yPy lattice matching GaAs substrate and AlxIn1-xSb1-yPy lattice matching InSb substrate for x and y = (0, 0.25, 0.50, 0.75, and 1) compositions were studied. The elastic constants C-11, C-12, C-44, and bulk, Young's, and shear modulus are also calculated. Meanwhile, the results were analyzed data in different pressure. The comparison between the calculated results and the available published data for quaternary alloys displayed that they had worthy accordance at pressure p = 0 and the results at P > 0 may be required as an acceptable reference.