In this chapter, we discuss solving PDE-based BIPs in CUQIpy. We illustrate this through two examples. The first one uses CUQIpy library to set up and solve a heat equation-based BIP. The second example uses the CUQIpy-FEniCS plugin to interface CUQIpy with FEniCS for modeling and solving PDEs using the finite element method. The latter example sets up and solves a 2D Poisson equation-based BIP.