A large flood event commonly leads to rapidly rising river stages and significant exchanges of water, sediment, and nutrients across the aquifer-river interface. Existing studies for surface-groundwater exchanges induced by flood events usually limit to a river-aquifer cross-section that is perpendicular to river channels, and neglect groundwater flow in parallel with river channels. Surface-groundwater exchanges to a flood event are investigated with specific considerations of unconfined flow in direction that is in parallel with river channels. The groundwater flow is described by a two-dimensional Boussinesq equation and the flood event is described by a diffusive-type flood wave. In addition, the effects of floodplain slope is considered. Analytical solutions are derived and tested using the numerical solution. The results indicate that river water infiltrates into aquifers quickly during flood events, and mostly returns to the river within a short period of time after the flood event. However, the rest river water will stay in aquifers for a long period of time. The residual river water not only flows back to rivers but also flows to downstream aquifers. The return flow induced by the flood event has a power-law form with time and has a significant impact on the base flow recession at early times. The solution can match the observed hydraulic heads peaks during flood events.