A novel method for extracting linear streets from a street network is proposed where a linear street is defined as a sequence of connected street segments having a shape similar to a straight line segment. Specifically a given street network is modeled as a Conditional Random Field (CRF) where the task of extracting linear streets corresponds to performing learning and inference with respect to this model. The energy function of the proposed CRF model is submodular and consequently exact inference can be performed in polynomial time. This contrasts with traditional solutions to the problem of extracting linear streets which employ heuristic search procedures and cannot guarantee that the optimal solution will be found. The performance of the proposed method is quantified in terms of identifying those types or classes of streets which generally exhibit the characteristic of being linear.Results achieved on a large evaluation dataset demonstrate that the proposed method greatly outperforms the aforementioned traditional solutions.