Self-adhesion, or clumping, primarily occurs in bio-inspired dry-adhesives when two or more adjacent fibers become in contact and adhere to each other due to large van der Waals (vdW) intermolecular forces. Studying self-adhesion is of primary interest as dry-adhesives drastically lose their adhesion strength after few load cycles if clumping occurs. An optimization procedure to select material properties, shape, and geometry of the fibers is therefore highly desirable for both improving the adhesion and reducing the probability of clumping. Few numerical models have been utilized to attain optimal geometry and material parameters. These models are developed based on the small-deflection beam theory and use an over-simplified elastic-contact model to determine adhesion forces. In this work, a model suitable to simulate large deformations with distributed intermolecular forces is proposed. The model is based on the finite element method (FEM) and uses an adaptive meshing procedure to accurately calculate adhesion forces. By using this model, clumping is studied and predictions are compared against experimental results obtained from the literature. In addition to the FEM model, an analytical model that considers large-deflection reactions of fibers is proposed to corroborate finite element results. Results from analytical and finite element models show precise clumping predictions.