Elastomers are widely used in components that are subject to compressive loading, such as bearings, mountings, O-rings, and other sealing or cushioning applications. Although standard test methods for characterizing compressive properties (such as ASTM D575-91 [2024], Standard Test Methods for Rubber Properties in Compression) allow for the comparative analysis of different materials, they often do not produce true material properties because of the influence of sample aspect ratio on measured stiffness during bonded compression. Well-known correction factors may be used to account for this dependence, but are typically only applicable to linear materials. This study develops a simple method for extracting nonlinear compressive material properties from bonded uniaxial compression tests of incompressible materials. The method involves using corrections to shift measured nonlinear stress–strain data before fitting with a nonlinear model of choice and was applied to a series of solid polyurethane (PU) cylindrical samples. Finite element models constructed using the extracted material properties show excellent agreement with the measured axial stress–strain and maximum radial strain data, and further validation is performed by successfully predicting the mechanical response of structured cylindrical solid PU samples containing air inclusions of various geometries.