The paper presents analytic expressions of the Helmholtz free energy and characteristic elastic deformation quantities such as the elastic moduli E, K, G and the elastic constants C11, C12, C44 for BCC interstitial and substitutional alloy with four components are determined by the statistical moment method. The obtained elastic quantities depend on temperature, pressure, the concentration of interstitial atoms, and the concentration of substitutional atoms. This is the elastic deformation theory of BCC interstitial and substitutional alloy with four components published for the first time. The elastic deformation theories of BCC metal, BCC binary interstitial alloy, BCC binary substitutional alloy, and BCC ternary interstitial and substitutional alloy are limit cases of the elastic deformation theory of BCC substitutional and interstitial alloy with four components. Our numerical calculations of the obtained theoretical results for metal Fe and alloy FeSi are in good agreement with other calculations and experiments. Other numerical calculations for alloys FeCr, FeNi, FeCrSi, FeNiSi, FeCrNiSi (some atoms Fe are substituted by atoms Cr and some other atoms Fe are substituted by atoms Ni) called stainless steels predict and orient experimental results in the future. Our numerical calculations for alloy FeCrNiSi are published for the first time.