Ellipsoidal BGK model is a general version of the BGK model where the local Maxwellian is generalized to a ellipsoidal Gaussian with a Prandtl parameter $\nu$ so that the model can produce the correct transport coefficient in the Navier-Stokes limit. In this talk, we consider the existence and uniqueness of stationary solutions for ES-BGK model in a slab imposed with the mixed boundary conditions. In the non-critical case $-1/2<\nu<1$, we estimate the temperature tensor using the equivalence relation with the temperature. In the critical case, $\nu=-1/2$, where such equivalence relation breaks down, we utilize the fact that the size of bulk velocity in $x$ direction can be controlled by the discrepancy of boundary flux, and estimates the difference between the total energy and the directional energy to estimate the temperature tensor, to bound the temperature tensor from below. This is a joint work with Stephane Brull