We propose a sparse representation approach for classifying different targets in Synthetic Aperture Radar (SAR) images. Unlike the other feature based approaches, the proposed method does not require explicit pose estimation or any preprocessing. The dictionary used in this setup is the collection of the normalized training vectors itself. Computing a sparse representation for the test data using this dictionary corresponds to finding a locally linear approximation with respect to the underlying class manifold. SAR images obtained from the Moving and Stationary Target Acquisition and Recognition (MSTAR) public database were used in the classification setup. Results show that the performance of the algorithm is superior to using a support vector machines based approach with similar assumptions. Significant complexity reduction is obtained by reducing the dimensions of the data using random projections for only a small loss in performance.