We present a numerical simulation for the blow molding of an industrial high density polyethylene part. The rheology of the polymeric material is described by means of an integral viscoelastic fluid model with a multi-mode relaxation spectrum. A membrane element is applied for performing the blow molding simulation of geometrically complex objects such as a bottle with a handle; the motion governing equations are described by means of a Lagrangian representation. The contact between the parison and the moving mold is handled by means of a robust algorithm. The numerical tool is applied for the production of a bottle with a handle. The predicted results are compared with their experimental counterparts. In particular, we focus on the thickness distribution of the blow product.