The stability of the Rayleigh-Taylor model for an electroviscoelastic Maxwell fluid are investigated. The method of multiple scales is used in order to obtain the stability conditions. A transcendental dispersion relation is obtained at zero-order. The special case, when the two fluids have the same kinematic viscosity, is considered to relax the complexity of the transcendental dispersion relation. The solvability conditions introduce a first-order differential equation. It is found that the increase in the relaxation time lambda has a destabilizing influence. Also the increase in the kinematic viscosity in the presence of the parameter lambda yields a destabilizing effect. The increase in the kinematic viscosity in the absence of elasticity (pure viscous fluids) has a stabilizing effect.