This chapter introduces a reduced stochastic fluid-structure interaction (FSI) model, where the full coupled dynamics are captured by a single stochastic viscous wave equation for the structure displacement. Unlike fully coupled stochastic FSI systems (studied later), this simplified model allows for explicit analysis using fundamental solutions, Fourier methods, and stochastic integration. The model considers a viscous incompressible fluid (stationary Stokes equations) interacting with an elastic membrane subjected to space-time white noise. Due to the geometry and linear coupling, the fluid’s effect on the structure is encoded via a Dirichlet-to-Neumann operator, yielding the stochastic viscous wave equation on \(\mathbb {R}^{2}\) . Key results include the following: While distinct from the splitting schemes used earlier, this model’s analysis provides foundational insights into stochastic FSI and showcases techniques for handling space-time white noise.