Magnetic Resonance Elastography (MRE) is a non-invasive imaging modality that quantifies the mechanical properties of soft tissues by measuring their response to low-frequency mechanical excitation. In brain MRE, the viscoelastic nature of parenchymal tissue and the presence of cerebrospinal fluid (CSF) play a significant role in wave propagation and stiffness estimation. Experimental evidence indicates that CSF motion alters measured displacement fields and affects stiffness quantification near fluid–solid boundaries [1], yet most existing numerical models neglect the explicit fluid dynamics of CSF. In this work, we introduce a three-dimensional finite element scheme formulated in the frequency domain that couples the viscoelastic solid mechanics of brain tissue with Stokes flow for CSF, which is appropriate for the low excitation frequencies employed in MRE. The brain parenchyma is modeled as a linear viscoelastic medium, while CSF is represented as an incompressible Stokes fluid, with dynamic and kinematic coupling enforced across fluid–solid interfaces. The coupled problem is solved on anatomically realistic brain geometries to simulate steady-state shear wave propagation and CSF motion simultaneously. The proposed framework provides a physics-based forward model for the generation of synthetic elastography data and is well suited for integration with data assimilation and reconstruction methodologies [2] that aim to infer tissue mechanical properties. By explicitly accounting for CSF–brain interaction, this work bridges a critical gap in current MRE modeling approaches and paves the way toward improved stiffness estimation in the presence of cerebrospinal fluid.