In this paper, a novel model based on the boundary element method (BEM) is presented for the hydrodynamic analysis of floating twin-hull structures carrying photovoltaic panels, supporting the study of wave responses and their effects on power performance in variable bathymetry regions. The analysis is restricted to two spatial dimensions for simplicity. The method is free of any mild-slope assumptions. A boundary integral representation is applied for the near field in the vicinity of the floating body, which involved simple (Rankine) sources, while the far field is modeled using complete (normal-mode) series expansions that are derived using separation of variables in the constant depth half-strips on either side of the middle, non-uniform domain, where the depth exhibited a general variation, overcoming a mild bottom-slope assumption. The numerical solution is obtained by means of a low-order panel method. Numerical results are presented concerning twin-hull floating bodies of simple geometry lying over uniform and sloping seabeds. With the aid of systematic comparisons, the effects of the bottom slope and curvature on the hydrodynamic characteristics (hydrodynamic coefficients and responses) of the floating bodies are illustrated and discussed. Finally, the effects of waves on the floating PV performance are presented, indicating significant variations of the performance index ranging from 0 to 15% depending on the sea state.