The electrically conductive composites having continuous structure of conductive particles with the continuous or network structure were designed and fabricated in the fiber-reinforced plastics (FRP) and the ceramics-matrix composites (CMCs). These self-diagnosis functions were evaluated from the measurement of resistance changes with applied strain in normal or cyclic loading tests. The practicability of the function was examined in bending tests for mortar specimen embedding FRP. Percolation phenomena with the second phase of various aspect ratios were also studied by two-dimensional computer simulation. The self-diagnosis functions of the CMC were evaluated by simultaneous measurements of stress and electrical resistance change as a function of applied strain in four-point bending tests. The chapter investigates the two-dimensional computer simulation to design percolation structure of the second phases with different aspect ratios. That is to clarify the relation between formation of percolation structure, the morphology, and the configuration of the second phase.