This chapter presents a co-axial, one-dimensional, time-dependent mathematical model for the dynamics of cerebrospinal fluid (CSF) in the spinal canal, coupled with the dynamics of the deformable spinal cord. The model may prove useful for a range of pathologies associated with disturbed CSF fluid dynamics. Two examples include Chiari malformations and syringomyelia, both of which are linked to anomalous CSF flow in the spinal subarachnoid space. Another relevant condition involves visual impairment due to disturbed CSF dynamics in the optic nerve sheath, coupled with the deformable optic nerve. The model could also be applied to simulate CSF/ISF flow in the perivascular spaces surrounding penetrating arterial and venous vessels in the brain or spinal cord. The one-dimensional, co-axial model presented here consists of four non-linear, time-dependent partial differential equations. Mathematically, these equations have some special characteristics. First, they cannot be expressed in conservation-law form, which creates the challenge of defining discontinuous solutions that obey the classical Rankine-Hugoniot conditions. Second, the non-conservative nature of the equations restricts the range of suitable numerical methods for solving them. Moreover, the equations are of mixed elliptic-hyperbolic type, which could make the problem potentially ill-posed. Fortunately, mathematical analysis of the system reveals a sufficiently large parameter region in which the equations are hyperbolic, ensuring that the system is well-posed. The model has also been coupled with the CSF dynamics in the cranial cavity within the framework of the global, closed-loop mathematical model for the human circulation. Preliminary results are promising. The chapter concludes with a selection of references for further study.