A two-dimensional semi-analytical solution to analyse stream-aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two-dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non-dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one-dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water-level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water-level variations due to stream and tidal boundaries are sensitive to specific yield.