We examine the effects of turbulence on elliptic instability of rotating stratified incompressible flows, in the context of the Lagrangian-averaged Euler–Boussinesq-α (LAEB-α) model of turbulence. We find that the LAEB-α model alters the instability in a variety of ways for fixed Rossby number and Brunt–Väisälä frequency. First, it alters the location of the instability domains in the (γ,cosθ)-parameter plane, where θ is the angle of incidence the Kelvin wave makes with the axis of rotation and γ is the eccentricity of the elliptic flow, as well as the size of the associated Lyapunov exponent. Second, the model shrinks the width of one instability band while simultaneously increasing another. Third, the model introduces bands of unstable eccentric flows when the Kelvin wave is two dimensional. We introduce two similarity variables—one is a ratio of the Brunt–Väisälä frequency to the model parameter Υ0=1+α2β2 and the other is the ratio of the adjusted inverse Rossby number to the same model parameter. Here, α is the turbulence correlation length and β is the Kelvin wave number. We show that by adjusting the Rossby number and Brunt–Väisälä frequency so that the similarity variables remain constant for a given value of Υ0, turbulence has little effect on elliptic instability for small eccentricities (∣γ∣⪡1). For moderate and large eccentricities, however, we see drastic changes of the unstable Arnold tongues due to the LAEB-α model. Additionally, we find that introducing anisotropy in the vertical component of the transported velocity field merely alters the definition of the model parameter Υ0, which effectively reduces the original parameter value. When the similarity variables are viewed with the new definition, the results are similar to those for the isotropic case.