A cross-head die in which the manifold is provided with means for selectively varying the volume of the manifold at some locations relative to other locations, whereby the relative wall thickness about the annular configuration of the material flowing through the die is selectively adjusted about the periphery of the annular configuration of flowing material. Wall thickness and configuration are further controlled at the outlet orifice of the die by means movable to selectively expand, contract and alter the annular configuration of the die passage at the orifice.