Humans can perceive external forces applied on a grasping tool based on skin pressure distribution at multiple contact areas during grasp. The authors have tried to represent external forces and torques by controlling the skin pressure distributions using suction stimuli and confirmed the potential but in a heuristic manner. In this paper, we investigate an improved method of skin stimulation based on a combination of psychophysical experiments and mechanical simulation. We focus on a simplification method of the complex strain energy density (SED) distribution at the contact areas with four quadrant values (SED index). The relationship between suction pressure and SED index was achieved by connecting the experiment and the mechanical simulation. We confirmed that a suitable SED index could represent the magnitudes of forces in multiple directions with a linear function. Experimental results also showed that the proposed method could represent arbitrary directions between pairs of the orthogonal axes.