Tubular networks of the endoplasmic reticulum (ER) are dynamic structures whose steady-state conformations are maintained by a balance between the persistent generation and vanishing of the network elements. While factors producing the ER tubules and intertubular junctions have been investigated, the mechanisms behind their elimination remained unknown. Here, we addressed the ER ring closure, the process resulting in the tubule and junction removal through constriction of the network unit cells into junctional knots followed by the knot remodeling into regular junctions. We considered the ring closure to be driven by the tension existing in ER membranes. We based our consideration on the notion of Gibbs’ thermodynamic tension and reviewed its relationship to other tension definitions used in the literature. We modeled, computationally, the structures of the junctional knots containing internal nanopores and analyzed their tension dependence. We analyzed the process of the pore sealing through membrane fission resulting in the formation of regular junctions. Considering the hemi-fission as the rate-limiting stage of the fission reaction, we evaluated the membrane tensions guaranteeing the spontaneous character of the pore sealing. We concluded that feasible membrane tensions explain all stages of the ER ring closure.