Mixture models are frequently used for modeling complex data. An extension of the EM algorithm, here called ECME, is proposed to compute the maximum likelihood estimate of parameters of symmetric -stable mixture model (S SMM). Comprehensive simulation studies are performed to show the performance of the proposed ECME algorithm. The robustness of the S SMM is investigated by simulations when it is used to model data generated from mixture of exponential power and t distributions. Both proposed ECME and Bayesian approaches are applied to three sets of real data, which shows that the proposed ECME algorithm outperforms the Bayesian paradigm for all three sets. Also, the S SMM is compared with the mixture of normal, skew normal, t, and skew t distributions for modeling four sets of real data. It turns out that the S SMM works as well as or better than above models. This can be considered as S SMM capability in robust mixture modeling.