The design for cold extrusion dies is very important, because the die insert is subjected to very high radial and hoop stresses. The design of cold extrusion dies has many constrained conditions. In this paper, the used assumptions are such that the yield strength of each ring is selected according to the allowable tensile or compressive hoop stress in each ring and the maximum allowable inner pressure, when yielding occurs in one ring of the dies, is obtained by the proposed equation. In order to obtain design variables, such as diameter ratios and interferences, using the maximum inner pressure, the flexible tolerance method was used for shrink-fitted thick-walled cylinders. ANSYS APDL was used to perform the repeated analysis of deformation of the dies due to the variation of the design variables. The response surface methodology is utilized to analyze the relationship between the design variables and the maximum radial displacement of the die insert during extrusion. From the results, it is found that outer diameter of the die insert has the largest effect on the minimization of maximum radial displacement at the inner surface of the dies.