The breakup during the extension of a low-density polyethylene Lupolen 1840D, as observed experimentally by Burghelea et al. (J Non-Newt Fluid Mech 166:1198-1209 2011), was investigated. This was observed during the extension of an circular cylinder with radius R (0) = 4 mm and length L (0) = 5mm. The sample was attached to two flat end plates, separated exponentially in time to extend the samples. A numerical method based on a Lagrangian kinematics description in a continuum mechanical framework was used to calculate the extension of an initially cylindrically shaped sample with and without small long-waved and centrally located suppression in the surface. The flow properties of the branched polymer melt were defined by a multi mode version of the molecular stress function constitutive equation. A multi mode version based on a Maxwell relaxation spectrum was applied, and the involved parameters were fitted based on previous measured extensional viscosities including the startup, relaxed and reversed flow of the Lupolen 1840D melt. For an ideal cylindrically shaped geometry, at some of the extensional rates, there was a match with the calculated break of strain values, but most were just below the error bars as reported experimentally by Burghelea et al. (J Non-Newt Fluid Mech 166:1198-1209 2011). At low extensional rates, the measurements were considerably above the calculated ones. A very small relative suppression in the surface (0.1%) was required to achieve an agreement with all measurements on average. The largest sensitivity to the surface suppression was at low extensional rates.