The compounds with general formula Mn+1AXn, where n = 1, 2, 3,…, where M = early transition metals, A = IIIA and IV A group elements like Al, Ga, In or Si, Ge and X = B, C or N for n = 1 and B or C or N for n greater than 1 are known as the compounds having MAX phases. These compounds (MAX phases) are having great potential for many technological applications due to their metallic and ceramic properties along with rare mechanical and chemical properties like damage and oxidation resistance, good thermal and electrical conductivity, reversible deformation and many more. The systematic and detailed study of these compounds gives the knowledge regarding their properties and hence we can search the new compounds for our technological needs. In the present paper, we have made a detailed investigation of the structural, electronic, optical and elastic properties of newly predicted MAX phase compounds Ti2BrB, Ti2BrC and Ti2BrN and also compared the results with the help of first-principles density functional theory. We have found that newly proposed MAX phase compounds Ti2BrB, Ti2BrC and Ti2BrN are chemically and mechanically stable. But the compound Ti2BrC is dynamically stable while the compounds Ti2BrB and Ti2BrN are dynamically unstable.