Phase contrast MR in patients with the Chiari I malformation demonstrates abnormal CSF flow in the foramen magnum and upper cervical spinal canal, related to abnormal pressure gradients. The purpose of this study was to analyze the role of CSF pressure in the pathogenesis of syringomyelia, with computational models. The spinal cord was modeled as a cylindrical poro-elastic structure with homogenous and isotropic permeability. The permeability was then made heterogeneous and anisotropic to represent the different properties of the central canal, gray and white matter. Fluid with a defined pressure, varying both in time and space, was prescribed in the SAS. Simulations were performed to quantify deformations and fluid movement within the cord. In the simulations with uniform permeability fluid moved into the cord in regions of higher pressure and out of the cord in regions of lower pressure. With permeability differences simulating gray and white matter the pattern was more complex, but similar. Adding the central spinal canal, fluid moved into the cord as in the previous case. However, preferential flow along the central canal hindered fluid from flowing back into the SAS. Pressure gradients in the SAS produce movement of fluid in the spinal cord. Assuming different relative permeability in gray matter, white matter and the central spinal canal, abnormal CSF gradients lead to accumulation of fluid within and adjacent to the spinal cord central canal.