The quantitative prediction of the adhesion strength of soft polymer tapes is a difficult fundamental problem, at the frontier between fracture mechanics, rheology, and polymer physics and chemistry. Besides, the possibility of this prediction is a strong industrial challenge. During the detachment of a soft polymer adhesive, the unconfinement of the thin layer of adhesive material most often leads to a process of cavitation or fingering of the detachment front. The scenario then continues with the creation of microscopic fibrils of adhesive material followed by their stretching until they debond. The key theoretical element currently missing to build a predictive model for the adhesion strength is the understanding of the individual fibril detachment criterion. The M2 internship and the following PhD thesis will be dedicated to the understanding of the debonding process of micrometric fibrils of soft adhesive material.