Viscoelastic materials are widely used for vibroacoustic solutions due to their ability to dissipate energy and thus mitigate vibrations and structure-borne sound. Wave propagation methods belong to a growing family of material characterization techniques based on the analysis of waveform patterns in one-dimensional structures. The time evolution of patterns results from material elasticity and damping. Conversely, it is possible to identify these properties once the pattern's time evolution is known. The most frequently used propagation methods, namely, Hopkinson bar methods, assume no dispersion, i.e., the complex elasticity modulus is not frequency dependent. However, this is not relevant for resilient materials such as elastomers. More recent approaches have been developed to measure frequency-dependent properties from a pulse propagating in a slender bar. In the previous works, we showed how to adapt these methods for shorter samples of materials. This represented a real advance, as extrusion is a cumbersome process for many materials. The main concept was to reconstruct the time history of the wave propagating in a composite structure composed of a long incident bar made of a known material and extended by a shorter sample bar. The sample material's viscoelastic properties were then determined in the frequency domain by optimization and wave fitting in the time domain. In industry, most insulation solutions that rely on mounts and bushings have to support structural weights. Consequently, it is particularly useful to measure the tangent viscoelastic properties of the material around the static stressed state and not only in stress-free conditions. Measuring strained materials not only requires modifying the experimental apparatus but also extending the scope of the underlying theory as the waves propagate differently in composite structures made of strained media. Here, we show how to overcome this challenging issue. The theoretical framework and its numerical implementation are described, and the method was validated experimentally by characterizing an elastomer sample under prestrained conditions.