In liquid composite molding processes, the compaction characterization of fibrous reinforcements plays a key role in determining the thickness, fiber volume content, and part shape. This study presents detailed experimental and modeling work to study the viscoelastic compaction response of three different types of 3D woven carbon fiber reinforcements, namely, orthogonal, angle interlock, and layer-to-layer, each having a different weave style and z-binder yarn pattern. For all reinforcements, single-step, multistep and cyclic compaction experiments were conducted. A nonlinear viscoelastic model is presented that accounts for large deformations and viscous effects, to capture the response of the material under various loading histories. Model verification is also presented to capture each response with separate sets of material parameters. Parametric studies are also performed to analyze the role of model parameters on the response of different types of loadings. X-ray computed tomography analysis showed significant permanent deformation of z-binder yarns through the thickness of the reinforcements. The comparison of modeling results with the experimental data show that the model is able to capture the stress decay after multiple compaction cycles, yet needs further investigations to predict complete cyclic hysteresis. However, model results agree reasonably well with the single and multistep compaction loading.