The recently developed phase-field evolution within the Representative Crack Element framework has been demonstrated to yield physically reasonable crack kinematics, including crack opening, closing, shearing as well as mixing aforementioned deformations. The work at hand presents cohesive fracture by elaborating phase-field modeling within the Representative Crack Element approach. A traction–separation law is postulated in the crack surfaces of the Representative Crack Element, which phenomenologically leads to cohesive adhesion in the RCE description. According to a continuous interpretation of an intact material and a fully broken material by the phase-field degradation function, a realistic material status is obtained with respect to different loading states, i.e. an opening or a shearing crack leads to cohesive adhesion failure but closing crack only shows a physical material contact behavior. This methodological constitutive relation is based on a straightforward variational approach and is derived out of the virtual power principles from both the RCE and the continuous descriptions. The unknown crack deformations are consistently resolved by a minimization algorithm of the RCE virtual power. Implemented into the context of the Finite Element Method framework, several demonstrative numerical examples are investigated. Some meaningful findings are pointed out and potential perspectives are proposed to consequently close this paper.