After placement of a soft contact lens onto the cornea, the upper eyelid deforms and settles the lens by squeezing fluid out of the post-lens tear film or POLTF (i.e., the tear fluid layer sandwiched between the lens and the cornea). This paper studies the physical mechanisms that control the dynamic state of the contact lens during blinking, i.e., its shape and its distance from the cornea, especially a long time after insertion. We model the lens as a deformable elastic shell and the cornea as a flat nondeformable body. The tear fluid is assumed to be Newtonian, and the lens is characterized by an elastic modulus and a Poisson ratio. Lubrication equations under creeping flow are used to solve the fluid problem, while the thin-shell approximation is applied to the solid lens. The solid and fluid mechanics problems are coupled by maintaining continuity of stress and velocity at the solid/liquid interface. Lid applied pressure causes the lens to approach the cornea by squeezing tear fluid out and also leads to the deformation of the lens. Subsequently, in the interblink period, since there is no applied force, the elastic energy stored in the lens due to its deformation is released causing it to move away from the cornea by imbibing tear fluid into the POLTF. If the POLTF thickness is large, the inward motion of the lens in the blink is more than the outward motion during interblink, and this causes the lens to settle closer to the cornea. Eventually, there may be a balance of the inward motion during the blink and the outward motion during the interblink. If so, the lens subsequently exhibits periodic steady-state motion. However, it is also possible that a balance of inward and outward motion is never achieved, and the lens continues to settle endlessly. If this happens, then the thin-film interactions between the mucin-covered corneal surface and the lens material determine whether the lens actually touches the cornea and possibly adheres. Our elastohydrodynamic analysis serves as a useful tool to elucidate the effects of various lens parameters on the final settled state of the lens. In particular, we are concerned about eventual adherence and/or mechanical abrasion to the cornea, which is very important to the ocular health of soft contact lens wearers.