The subarachnoid space is a layer in the meninges that surrounds the brain and is filled with trabeculae and cerebrospinal fluid. Quantifying the volume and thickness of the subarachnoid space is of interest in order to study the pathogenesis of neurodegenerative diseases and compare with healthy subjects. We present an automatic method to reconstruct the subarachnoid space with subvoxel accuracy using a nested deformable model. The method initializes the deformable model using the convex hull of the union of the outer surfaces of the cerebrum, cerebellum and brainstem. A region force is derived from the subject's T1-weighted and T2-weighted MRI to drive the deformable model to the outer surface of the subarachnoid space. The proposed method is compared to a semi-automatic delineation from the subject's T2-weighted MRI and an existing multi-atlas-based method. A small pilot study comparing the volume and thickness measurements in a set of age-matched subjects with normal pressure hydrocephalus and healthy controls is presented to show the efficacy of the proposed method.