A computational algorithm based on the Principle of Minimum Total Energy subjected to a Stress Condition (PMTE-SC) is used to analyse the debonding along the fibre-matrix interface under transverse loads. This algorithm is implemented in a 2D plane strain finite element model using the Abaqus software. The behaviour of the fibre-matrix interface is modelled using a damageable linear-elastic spring distribution by means of a User Material subroutine (UMAT). The numerical model considers an isolated glass fibre embedded in an epoxy matrix under remote transverse tension. The algorithm performs a quasistatic time-stepping procedure that minimizes the total energy functional given by the sum of the potential and dissipated energy. Particular attention is paid to the discussion about the symmetrical and non-symmetrical character of the debond onset and growth as a function of the interface and bimaterial system parameters. The numerical results indicate close agreement with previous analytical studies. The algorithm is able to predict the remote load necessary to originate the onset of the debond and its length.