In the study described in this article, we aimed to apply multiparametric optimization to the processing conditions in a spider die used for the extrusion of polymers, in this case, high-density polyethylene tubes. Product quality is affected by the homogeneity of the flow speed and the temperature at the die exit. Inhomogeneity causes shape distortions and material weak spots (weld lines), and its major cause in spider dies is the discontinuity and distortion of the flow caused by spider legs, the ties by which the inner mandrel of the die is secured to its external casing. The NelderMead nonlinear optimization technique was applied to the numerical model to pinpoint the processing conditions, namely, the inlet pressure, inlet temperature of the melt, temperature of the die walls, and temperature of the spider legs. (C) 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012