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Abstract It is well known that there exists a threshold κc $\kappa_{{c}}$ such that the linearized stratified viscoelastic Rayleigh–Taylor problem is unstable for the elasticity coefficient κ satisfying κ<κc $\kappa <\kappa_{{c}}$. In this paper, we further prove that if κ<κc $\kappa <\kappa_{{c}}$, 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 $\kappa_{{c}}$. In addition, we further extend the obtained results in the linearized stratified viscoelastic Rayleigh–Taylor problem to the linearized stratified magnetic Rayleigh–Taylor problem.