A compliance operator is often utilized to evaluate the elastic displacement of surfaces in the simulation of transient and steady-state elastohydrodynamic lubrication of conformal-contact systems. The values of the compliance operator represent the elastic responses of all nodes when only one node is under a unit load. The accuracy of compliance operator values, computational cost, and storage size are important issues. Our study of steady-state conformal-contact elastohydrodynamic lubrication analyses suggests a method of selective-fine-mesh with selective-storage, as well as a special technique of the combined selective-fine-mesh with selective-storage mapping. These two techniques enable an efficient elasticity procedure for the simulation of steady-state and transient conformal-contact elastohydrodynamic lubrication systems by means of the finite element method.