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Continuous nanofibers fabricated by the electrospinning technique have found increasing applications (e.g., nanofiber composites, nanofiber devices, bioengineering tissue scaffolding, etc.). For a nanofiber network subjected to a small external perturbation, the fiber segments within the network may deflect and stick to each other under the condition that their surface adhesion energy overcomes the elastic strain energy induced by fiber bending. Therefore, this paper aims to study adhesion-induced nanofiber collapse and relevant criteria. A simple fiber collapse model was proposed, which is based on the contact of two deflected elastic filaments under surface adhesion. Four fundamental fiber collapse modes (i.e., fiber-flat substrate, parallel fibers, orthogonal fibers and fibers at arbitrary angle) were considered, and corresponding collapse criteria were determined in explicit forms. Effects of fiber elasticity, surface adhesion and fiber geometries on the collapse criterion were explored in a numerical manner. Results show that for a fiber segment pair at a relatively large angle, the critical distance to induce the fiber collapse is independent of the fiber radius. This distance is a function of the fiber aspect ratio and the material intrinsic length (γ/E, where γ is the surface energy and E is Young’s modulus). The fiber collapse model developed in this study can be used as the theoretical basis for design and failure analysis of nanofiber networks and nanofiber devices, among others.