Presliding contacts play an important role in stiffness, damping, and thus dynamic response of assembled structures. Load-dependent nonlinearities in presliding contacts still hinder predictive modeling. Classical models apply only to smooth elastic contacts and a small subset of materials. Recently, the authors tested high density polyethylene (HDPE) inside a scanning electron microscope (SEM) and observed that nonlinearity trends in tangential stiffness and damping deviate from the predictions of the classical models. This discrepancy was attributed to HDPE’s nonlinear viscoplastic response. The aim of this study is to model aforementioned experiments numerically and investigate the influence of nonlinear material response on the presliding response of spherical contacts. A finite element model of a rigid spherical indenter pressed and sheared on a nonlinear viscoplastic half-space is constructed. The indenter geometry and boundary conditions are set in accordance with the experiments, and the constitutive model is tuned to the measured indentation responses. The tuned model delivers a shear response in agreement with the experiments. Accumulated plastic deformations are also found to correlate well with the wear profiles. The model further reveals that nonlinear viscoplasticity dominates tangential stiffness and dissipation at high normal preloads. Our results confirm further that nonlinear material response contributes significantly to the load-dependent nonlinearities in viscoplastic presliding contacts.