A vertical tensioned flexible sheet can function as a low-cost removable wave barrier, providing essential sheltering for coastal waters and floating facilities located behind it. In this study, we investigate the complex interactions between surface waves and a thin viscoelastic barrier that is only partially submerged, extending from the water surface into the water column. Three distinct materials: nonwoven geotextile, PA 6, and HDPE, are considered for barrier construction. Through comprehensive analysis, we evaluate the effects of these materials on wave attenuation, aiming to determine the optimal dimensions, tension, and material type for various coastal environments. Using the eigenfunction expansion method, the study reveals that wave transmission significantly decreases with increased rigidity of the barrier. Additionally, the viscous effects become more pronounced for barriers demonstrating greater flexibility. Notably, upon comparing the performance of the three materials, it is found that the HDPE barrier, designed with a draft constituting 40% of the water depth and a thickness of 15 cm, provides an excellent balance between effective wave attenuation and cost efficiency. These findings underscore the potential of using innovative materials in coastal engineering to enhance the resilience of marine infrastructure against wave action.