A Rankine source method is applied to predict linear and weakly nonlinear sectional loads of a modern container ship. The method uses solution in the frequency domain, linearized with respect to wave amplitude about the nonlinear steady flow due to forward speed, which accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Weak nonlinearity of the sectional loads in waves (e.g., hogging-sagging asymmetry) is taken into account by pressure extrapolation and integration up to the estimated actual water line. The sectional forces obtained with this method are compared with the results of other methods, including (1) linear Rankine panel method, where flow due to waves is linearized about the double-body flow, (2) linear zero-speed Green function method with correction for forward speed, (3) fully nonlinear simulations based on field-based solution of Reynolds-averaged Navier–Stokes (RANS) equations, and (4) model tests. Comparison with RANS solution and model tests shows, that the proposed method can accurately predict sectional loads for small to moderate wave heights.