The brain’s biomechanics are driven by a dynamic interplay between the tissue, blood, cerebrospinal fluid (CSF), and interstitial fluid and exhibit complex fluid flow and displacement patterns. Despite being essential to normal brain function, our understanding of intracranial dynamics is still limited, and various diseases are associated with impaired CSF flow and elevated intracranial pressure. Here, we present a computational model of cardiac-induced pulsatile motion inside the human cranial cavity. The CSF flow in the subarachnoid space and ventricular system is modeled using the time-dependent Stokes equations and coupled with Biot’s poroelasticity equations in the brain tissue, thus integrating all major intracranial constituents into the modeling approach. Employing the pulsatile inflow of blood into brain tissue as a driver of motion, the model enables us to study the dynamics of the entire intracranial system. In addition to the modeling aspects, we showcase the creation of volumetric multidomain meshes from surface meshes using fTetWild, use the FEniCS extension Multiphenics to solve monolithic multiphysics problems, and generate dynamic, interactive standalone animations of the obtained results with PyVista and K3D Jupyter.