Understanding the elastoplastic contact loading–unloading behavior between a sphere and a rigid plane is a problem in the field of contact mechanics. In this study, a bilinear strain-hardening material model was used to study the frictionless elastoplastic contact loading–unloading behavior of a sphere in contact with a rigid plane across a large range of interference. A two-dimensional axisymmetric finite element model was established. The effects of the tangent modulus (Et) and the ratio of the reduced elastic modulus to the yield strength (E/Y) on the contact load, residual interference, and contact area of the spherical contact model during loading–unloading were analyzed for a series of different interferences. The effects of Et and E/Y on the elastoplastic contact loading–unloading behavior were amplified with increasing interference. With an increase in Et, the effect of E/Y on the contact behavior was diminished. A new constitutive model for elastoplastic contact loading–unloading is presented. The model accommodates the calculation of the contact load, contact area, and residual interference of the spherical contact model across a large range of interference. The proposed model was verified by comparing its predictions with those of previous models. In the range of material properties considered in this work, the current research results can be applied to particle and contact mechanics.