This paper presents a direct time‐domain method for the prediction of symmetric hydroelastic responses of ships progressing with forward speed in small amplitude waves. A transient time‐domain free surface Green function is used for the idealisation of the seakeeping problem using an Earth fixed coordinate system. Free surface ship hydrodynamics are idealised in the time domain by a Green function, and forward speed effects are idealised by a space‐state model. Modal actions are accounted for by Timoshenko beam structural dynamics. Flexible fluid structure interaction (FFSI) coupling is enabled by a body boundary condition, and a direct integration Newmark‐β scheme is used to obtain symmetric dynamic responses. The method is validated against available published numerical and experimental results. A parametric study for different container ship hull forms confirms that (i) forward speed effects should be taken under consideration as far as practically possible and (ii) hull flexibility effects accounting for hull shear deformation and rotary inertia are more notable for slender hull forms.