The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the problem of discovering submatrices from the given matrix with bounded deviations from their low-rank approximations. We introduce an effective two-phase method for this task: first, we use sampling to discover small nearly low-rank submatrices, and then they are expanded while preserving proximity to a low-rank approximation. An extensive experimental evaluation confirms that the method we introduce compares favorably to existing approaches.