This paper studies mixture modeling using the Elliptical Gamma distribution (EGD)—a distribution that has parametrized tail and peak behaviors and offers richer modeling power than the multivariate Gaussian. First, we study maximum likelihood (ML) parameter estimation for a single EGD, a task that involves nontrivial conic optimization problems. We solve these problems by developing globally convergent fixed-point methods for them. Next, we consider fitting mixtures of EGDs, for which we first derive a closed-form expression for the KL-divergence between two EGDs and then use it in a’‘split-and-merge’’expectation maximization algorithm. We demonstrate the ability of our proposed mixture modelling in modelling natural image patches.