This work presents a novel approach for the rapid segmentation of clinically relevant subcortical brain structures in T1-weighted MRI by utilizing a shape-constrained deformable surface model. In contrast to other approaches for segmenting brain structures, its design allows for parallel segmentation of individual brain structures within a flexible and robust hierarchical framework such that accurate adaptation and volume computation can be achieved within a minute of processing time. Furthermore, adaptation is driven by local and not global contrast, potentially relaxing requirements with respect to preprocessing steps such as bias-field correction. Detailed evaluation experiments on more than 1000 subjects, including comparisons to FSL FIRST and FreeSurfer as well as a clinical assessment, demonstrate high accuracy and test-retest consistency of the presented segmentation approach, leading, for example, to an average segmentation error of less than 0.5mm. The presented approach might be useful in both, research as well as clinical routine, for automated segmentation and volume quantification of subcortical brain structures in order to increase confidence in the diagnosis of neuro-degenerative disorders, such as Alzheimer's disease, Parkinson's disease, Multiple Sclerosis, or clinical applications for other neurologic and psychiatric diseases.