This study describes modeling and computational analysis technique for design of humanoid head that can generate human-like facial expression. Current humanoid prototypes utilize either traditional servo motors or other form of bulky actuators such as air muscles to deform soft elastomeric skin that in turn creates facial expression. However, these prior methods have inherent drawbacks and do not resemble human musculature. In this paper, we report the advances made in design of humanoid head using shape memory alloy actuators. These muscle-like actuators are often in discrete form and finite in number. This brings up the fundamental question regarding their arrangement and location of terminating and sinking points for each action unit. We address this question by developing a Graphical Facial Expression Analysis and Design (GFEAD) technique that can be used to optimize the space, analyze the deformation behavior, and determine the effect of actuator properties. GFEAD will be described through generic mathematical models and analytical geometry confining the discussion to two-dimensional planes. The implementation of the graphical method will be presented by considering different practical cases.