In this paper we address the problem of robust face recognition by formulating the pattern recognition task as a problem of robust estimation. Using a fundamental concept that in general, patterns from a single object class lie on a linear subspace (Barsi and Jacobs, 2003 [1]), we develop a linear model representing a probe image as a linear combination of class specific galleries. In the presence of noise, the well-conditioned inverse problem is solved using the robust Huber estimation and the decision is ruled in favor of the class with the minimum reconstruction error. The proposed Robust Linear Regression Classification (RLRC) algorithm is extensively evaluated for two important cases of robustness i.e. illumination variations and random pixel corruption. Illumination invariant face recognition is demonstrated on three standard databases under exemplary evaluation protocols reported in the literature. Comprehensive comparative analysis with the state-of-art illumination tolerant approaches indicates a comparable performance index for the proposed RLRC algorithm. The efficiency of the proposed approach in the presence of severe random noise is validated under several exemplary noise models such as dead-pixel problem, salt and pepper noise, speckle noise and Additive White Gaussian Noise (AWGN). The RLRC algorithm is found to be favorable compared with the benchmark generative approaches.