A theory of stability for deformation of BKZ viscoelastic bars is developed. This theory is an extension of the one given by Ericksen for elastic bars. For appropriate strain potentials under certain loads in uniaxial creep and constant rate of extension, the bar will deform homogeneously for some time, and then become unstable and neck. An example is given simulating the behavior of a linear polyethylene bar in creep and in constant rate of extension. For the sake of illustration, the data used at small deformations were obtained from actual experiments, but at higher stretches were hypothesized so as to give the points of instability as actually observed.