Two interface models based on physical considerations are proposed to analyze the free-edge effects in unidirectional multilayered composites. The first model is a transition behavior law describing the graded properties of the interlayer between two adjacent layers. It is defined according to the stacking direction and based on a microscopic analysis of the fiber distribution in the vicinity of the interlayer. Used in a numerical simulation, this model gives accurate stress distributions in the laminate, including the interlaminar stresses at the free-edge that are not singular. The second model utilizes an interface law, defined on the material surface, resulting from the asymptotic resolution of an elastic problem pertaining to the interlayer and simulating a very thin flexible layer. This model also gives no singular free-edge interlaminar stresses close to those obtained with the first model.