Purpose Chiari I malformation leads to abnormal cerebrospinal fluid (CSF) flow dynamics and often is accompanied by syrinx formation. Phase constrast MR investigations reveal that peak flow velocities increase, whereas the altered pressure gradients are much more difficult to assess noninvasively. In this study, we use computer simulations to investigate how tonsil herniation changes pressure dynamics and flow in the cervical subarachnoid space. Materials and Methods. A 3D mathematical model of the cervical subarachnoid space, with and without herniated tonsils, was used to simulate CSF flow dynamics over several cycles of sinusoidal flow. Simulation results for the case with herniated tonsils were compared with corresponing results for normally positioned tonsils, while keeping all other parameters the same. Results Tonsil herniation caused pressure gradients to increse both in the superior-inferior direction and in axial planes of the model. The change in pressure dynamics caused a more complex flow velocity pattern with higher peak velocities, pronounced synchronous bi-directional flow, and larger velocity components within axial planes. Conclusion Chiari I malformation increases pressure gradients and flow complexity in the cervical subarachnoid space. This implies, e.g., that the spinal cord-CSF interaction dynamics changes following tonsil herniation, something which might have a role to play in syrinx formation.