Active filamentous organelles such as cilia and flagella oscillate due to the interplay between activity, elasticity, and viscous hydrodynamic drag. The presence of no-slip boundaries also impacts the viscous drag forces on the filament. Recent efforts to develop low Reynolds numbers synthetic swimmers and mixers that mimic the ciliary dynamics have used effective elastic filaments that are animated. The instabilities underlying the spatiotemporal dynamics of such biomimetic filaments are dominated equally by elasticity and fluid-solid viscous interactions. Predicting ensuing patterns requires robust computational models that can capture both large-amplitude elastic deformation of the filaments and associated long-ranged hydrodynamic interactions. To address this coupled elastohydrodynamic problem, we develop a composite framework that combines a computational rod model valid for slender filaments and slender body theory (SBT) that accounts for hydrodynamic interactions. The presence of no-slip boundaries is accounted for by using a wall-corrected slender body theory (W-SBT). We analyze the accuracy of the slender body formulations and compare them to solutions obtained via computational fluid dynamic solvers. SBT and W-SBT are found to be computationally faster than other hydrodynamic models; however, they may not provide accurate solutions for small aspect ratio filaments. The fluid-structure interaction model we present here, provides a starting point to computationally investigate the movements of natural and biomimetic cilia and flagella in the vicinity of plane walls.