A new universal extensional rheometer, which makes it possible to investigate the elongational properties of polymer melts, is described. Measurements under a wide variety of constant stretching rates and constant tensile stresses can be undertaken and recoil and relaxation experiments can be performed on a small amount of material. The operation modes of the apparatus are demonstrated on a polystyrene sample. For this polystyrene the viscosity and the recoverable strain in the steady state of elongation were measured over more than three decades of the tensile stress. At small stresses the recoverable strain is proportional to the stress, i.e., the compliance is constant and the viscosity gives a constant value which is three times the zero‐shear viscosity. At higher stresses the recoverable strain seems to level off and the viscosity runs through a maximum which lies 30% above the stress‐independent value.