Contacts between different meshed components in a finite element model frequently present modeling challenges. Tracking the progress of contact and separation is computationally expensive and may result in non-convergence of the model. In many contact problems of practical interest, such as bolted assemblies or in a shaft bearing where the shaft is constrained against rotation, it is clear that the components are in essentially constant contact and relative motion between them is negligible. In these cases, we can reduce the computational burden by defining an interface between the bodies using modeling devices other than the surface element contact commands. Some approaches in common use, such as tying the meshed surfaces together, or applying fixed boundary condition constraints in various directions, while they resolve convergence issue, can result in non-physical stress distributions and unconservative results in some cases. In the present work, an approach is presented that makes use the non-linear spring elements included in Abaqus to model the contact of meshed components. The contact is modeled as springs with a bi-linear slope that are essentially rigid in the gap closing direction and essentially free in the gap opening direction. This method will be shown to be computationally faster in most cases, and yet yield substantially the same stress distributions as an actual model of the contact suing surface elements. The convergence issues sometimes encountered in contact problems are avoided. Additionally, it is possible to model contacts with significant gaps (prior to loads being applied) and interference fits. In most cases, the model based on springs was significantly faster running than the surface element contact-based model. Furthermore, the spring-based models approached the speed of simpler and lower fidelity constraint-based models.