In this paper, a robust facet model is developed, and applied to speckle noise removal in syntehetic aperture radar (SAR) images. The parameters of a facet model is usually estimated by a least-squares (LS) method under the Gaussian assumption. In many applications, such as speckle removal in SAR images, the noise process is not Gaussian, and conventional estimators do not work. A robust estimation algorithm is developed, and applied to remove speckle noise in synthetic aperture images. Conventional adaptive filtering approaches in speckle filtering smoothes the image selectively depending on the details of underlying textures, and tend to blur details after speckle removal. In the proposed approach, the image is assumed to be composed of structural and stochastic components, and the stochastic component is modeled by a robust facet model. The proposed method is applied to real synthetic aperture images to demonstrate the validity and effectiveness of the algorithm.