The presence of sediments near the Earth’s surface can significantly amplify the strength of shaking during earthquakes. Such basin or site amplification effects have been well documented in numerous regions, yet the complex and often situational dependence of competing reasons for this amplification makes it hard to quantify in a general sense or to determine the most significant contributions. Simple 1D seismic profiles can be used to estimate the amplitude differences between a basin site and a hard‐rock reference site, but this ignores any reflections or conversions at the basin edge or a resonance effect depending on the basin’s geometry. In this article, we explore an analytic model based on coupling coefficients for surface Rayleigh waves to account for the lateral discontinuities at a basin’s edge (Datta 2018). We use this simple tool to explore the relationship between the basin’s Rayleigh‐wave amplification spectrum and various parameters such as basin depth, edge slope angle, and impedance contrast. The step‐by‐step construction of the model allows us to quantify the contributions from various wave propagation effects with the goal of identifying situations under which various basin‐edge effects must be considered in addition to purely 1D estimates. For the most velocity contrasts (less than a factor of 5), the error made by the 1D theory in predicting maximum Rayleigh‐wave basin amplification is under 35% for both the horizontal and the vertical components. For simple basins, the vertical amplification dominates at larger high frequencies and the horizontal at lower frequencies. Finally, we demonstrate from comparisons with spectral‐element wavefield simulations that realistic velocity structures can be reduced to a simpler “box” shape for the semi‐analytic formulation used here with reasonable results. For the purposes of estimating site‐amplification or microzonation, an improved model that accounts for basin‐edge effects can be implemented without high‐computational cost.