In the hydroelastic analysis of large floating structures, the structural and hydrodynamic analyses are coupled, and the structural stiffness plays an important role in the accurate prediction of the response. However, there is usually a large difference between the longitudinal and the cross-sectional scales of modern ships, and the sectional configurations are generally complex, making it difficult to obtain the exact structural stiffness. Using a full finite element model to calculate the structural stiffness is inevitably time-consuming. Since modern ship structures are usually nearly periodic in the longitudinal direction, we treat the hull as a periodic Euler–Bernoulli beam and use a novel implementation of asymptotic homogenization (NIAH) to calculate the effective stiffness. This can greatly improve the computational efficiency compared with a full finite element model. Based on a combination of finite element and finite difference methods, we develop an efficient analysis technique to solve the hydroelastic problem for nearly-periodic floating structures. The finite element method is used to efficiently calculate the structural stiffness, and the finite difference method is used to solve the hydrodynamic problem. This proposed technique is validated through several test cases with both solid and thin-walled sections. A range of representative mid-ship sections for a container ship are then considered to investigate the influence of both transverse and longitudinal stiffeners on the structural deformations. A simple method for including non-periodic end effects is also suggested.