We derive the necking condition in isothermal melt spinning employing the model of convected Maxwell fluids with strain-rate dependent material relaxation time. It is found that necking is possible when the extensional viscosity is strain-thinning (strain-softening), and impossible when the extensional viscosity is strain-thickening (strain-hardening). This finding then immediately reveals the correspondence between the spinning process and entrance flow (contraction flow), as several recent articles show that vortex is formed in the entrance flow when the extensional viscosity is strain-thickening. Thus necking in spinning corresponds to no vortex in entrance flow, whereas no necking in spinning to vortex in entrance flow, for the flow mechanism of the both situations is the extensional flow whose behavior is determined by the extensional viscosity.