It　is　well　known　that　there　exists　a　threshold　κc　such　that　the　linearized　stratified　viscoelastic　Rayleigh–Taylor　problem　is　unstable　for　the　elasticity　coefficient　κ　satisfying　κ<　κc.　In　this　paper,　we　further　prove　that　if　κ<　κc,　then　there　exists　an　unstable　solution　to　the　linearized　stratified　viscoelastic　Rayleigh–Taylor　problem　with　a　largest　growth　rate.　Moreover,　the　largest　growth　rate　decreases　from　a　positive　constant　to　0　as　κ　increases　from　0　to　κc.　In　addition,　we　further　extend　the　obtained　results　in　the　linearized　stratified　viscoelastic　Rayleigh–Taylor　problem　to　the　linearized　stratified　magnetic　Rayleigh–Taylor　problem.　©　2018,　The　Author(s).