Multiple researchers have identified shoreline features, such as scarps, on Mars. These features occur in both paleocrater lake basins and the northern hemispheric basin. Here we use a simple numerical model to investigate the viability of forming Martian bedrock scarps via wind wave action. We use the Pierson-Moskowitz equation modified for Martian gravity to generate wave fields under a variety of wind speeds and use those wave fields to drive a terrestrial bedrock shore erosion model modified for Martian conditions. Our results indicate that even with conservative assumptions for the key parameters of wind speed, slope, and substrate, it is difficult to form shoreline features of sufficient magnitude to be captured by spacecraft imaging. Under many combinations of reasonable initial conditions, no shoreline features are formed. In cases where shoreline features do develop, the largest equilibrium scarp height is ~5 m, and the shorelines require nearly 2000 model years to form. In light of these results and the difficulty of maintaining warm, wet climates on Mars, it seems unlikely that the putative shoreline features identified in images are a result of water wave erosion, and alternative hypotheses, such as ice cover, should be entertained.