%X Hydroelastic waves propagating at a constant velocity at the surface of a fluid are considered. The flow is assumed to be two-dimensional and potential. Gravity is included in the dynamic boundary condition. The fluid is bounded above by an elastic sheet which is described by the Plotnikov-Toland model. Fully nonlinear solutions are computed by a series truncation method. The findings generalised previous results where the sheet was described by a simplified model known as the Kirchhoff-Love model. Periodic and generalised solitary waves are computed. The results strongly suggest that there are no true solitary waves (i.e., solitary waves characterised by a flat free surface in the far field). Detailed comparisons with results obtained with the Kirchhoff-Love model and for the related problem of gravity capillary waves are also presented. %O This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in: Gao, T; Vanden-Broeck, J-M; (2014) Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves. Physics of Fluids, 26 (8), Article 087101, and may be found at: http://dx.doi.org/10.1063/1.4893677. %L discovery1477287 %J Physics of Fluids %D 2014 %A T Gao %A J-M Vanden-Broeck %V 26 %T Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves %N 8