In supersymmetric E 6 the masses of the third family quarks and charged lepton, t − b − τ , as well as the masses of the vector-like quarks and leptons, D −D and L−L, may arise from the coupling 27 3 ×27 3 ×27 H , where 27 3 and 27 H denote the third family matter and Higgs multiplets respectively. We assume that the SO(10) singlet component in 27 H acquires a TeV scale VEV which spontaneously breaks U (1) ψ and provides masses to the vector-like particles in 27 3 , while the MSSM doublets in 27 H provide masses to t, b and τ . Imposing Yukawa coupling unification h t = h b = h τ = h D = h L at M GU T and employing the ATLAS and CMS constraints on the Z ψ boson mass, we estimate the lower bounds on the third family vector-like particles D −D and L −L masses to be around 5.85 TeV and 2.9 TeV respectively. These bounds apply in the supersymmetric limit.