The present paper proposes "Deformation Characteristics" (DC) as a new deformation measure of screw extrusion processes, based on the Green deformation tensor. In contrast to previous strain measures heuristically proposed by Mohr, et al., Mckelvey, and Pinto and Tadmor, the new DC can naturally incorporate the demixing phenomena and systematically take into account the three-dimensional circulatory flow with the screw flight effect. Therefore, DC can be regarded as an improved strain measure. "Weighted Average Deformation characteristics" (WADC) is also proposed to indicate the overall deformation characteristics as a quantitative measure to the "goodness of mixing" of the extrusion process. The present paper includes discussion on delicate differences between DC and several other strain measures in case of the two-dimensional velocity approximation, and on the application of DC into a general three-dimensional velocity field obtained by a quasi-three-dimensional finite element analysis of extrusion processes. In determining WADC in the three-dimensional application, the residence time distribution function, including the three-dimensional circulatory flow effect, is used.