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Although interest in the biomechanics of the brain goes back over centuries, mathematical models of hydrocephalus and other brain abnormalities are still in their infancy and a much more recent phenomenon. This is rather surprising, since hydrocephalus is still an endemic condition in the pediatric population with an incidence of approximately 1–3 per 1000 births. Treatment has dramatically improved over the last three decades, thanks to the introduction of cerebrospinal fluid (CSF) shunts. Their use, however, is not without problems and the shunt failure at two years remains unacceptably high at 50%. The most common factor causing shunt failure is obstruction, especially of the proximal catheters. There is currently no agreement among neurosurgeons as to the optimal catheter tip position; however, common sense suggests that the lowest risk location is the place that remains larger after ventricular decompression drainage. Thus, success in this direction will depend on the development of a quantitative theory capable of predicting the ultimate shape of the ventricular wall. In this paper, we report on some recent progress towards the solution to this problem.