Macro-scale delamination and micro-scale fiber-matrix debonding events may notably affect the mechanical performance of fibrous composite elements. This article presents a two-dimensional finite-element (FE)-based formulation of interface of a small but finite thickness relying on the so-called linear elastic-brittle interface model (LEBIM) to be applied for simulation of an adhesive interface debonding and fiber-matrix decohesion failures. This modeling strategy is implemented in the commercial FE package ABAQUS by means of the user-defined subroutine UMAT. The practicability of the developed interface model is assessed through the comparison of the computational results with experimental data and with previous boundary element method (BEM) analyses using the LEBIM formulation. Specifically, LEBIM results for the interlaminar fracture toughness test showed an excellent agreement with experimental results (adhesive saw-tooth post-peak response was captured). Besides, studies of several micro-mechanical fiber-matrix configurations showed that fiber-matrix debonding events are the predominant failure mechanisms for moderate transverse loading values. The developed tool will certainly contribute to elucidate several open aspects regarding the interface crack behavior in fiber-reinforced composite materials.