Uniaxial ring test is a widely used mechanical characterization method for a variety of materials, from industrial elastomers to biological materials. Here we show that the combination of local material compression, bending, and stretching during uniaxial ring test results in a geometry-dependent deformation profile that can introduce systematic errors in the extraction of mechanical parameters. We identify the stress and strain regimes under which stretching dominates and develop a simple image-based analysis approach that eliminates these systematic errors. We rigorously test this approach computationally and experimentally, and demonstrate that we can accurately estimate the sample mechanical properties for a wide range of ring geometries. As a proof of concept for its application, we use the approach to analyze explanted rat vascular tissues and find a clear temporal change in the mechanical properties of these explants after graft implantation. The image-based approach can therefore offer a straightforward, versatile, and accurate method for mechanically characterizing new classes of soft and biological materials.