Design problems using high fidelity numerical methods such as Finite Element Analysis (FEA) can be computationally intensive, especially if they require multiple runs for different loading conditions or varying parameters. Hence reduced-order models (ROM) which can reproduce the simulation results with high accuracy, while working at a very low computational budget are desirable. Subspace projection-based ROMs are widely used for the analysis of linear systems, using linear eigenmodes as projection basis and can be extended to nonlinear systems using empirical eigenmodes such as Proper Orthogonal modes (POM). However, problems involving moving contact are difficult to handle for such procedure due to moving boundary conditions of the underlying PDE. Here we use the approach proposed by  towards reduced-order dynamic analysis of Hyperelastic wheel rolling, incorporating the geometric and material nonlinearities in addition to contact with a view to extend it to tire rolling analysis. The simulations are performed using commercial Finite Element software Abaqus and the ROM based results are verified using Matlab and show a very good match for displacement and contact forces with a model that is orders of magnitude smaller than the full order system.