In this paper, we propose a finite mixture model of generalized Gaussian distributions (GDD) for robust segmentation and data modeling in the presence of noise and outliers. The model has more flexibility to adapt the shape of data and less sensibility for over-fitting the number of classes than the Gaussian mixture. In a first part of the present work, we propose a derivation of the Maximum-Likelihood estimation of the parameters of the new mixture model and we propose an information-theory based approach for the selection of the number of classes. In a second part, we propose some applications relating to image, motion and foreground segmentation to measure the performance of the new model in image data modeling with comparison to the Gaussian mixture.