Solids can not be infinitely stressed under all stress states, thus only certain portion of the stress space has significance for solids. The shape, size and structure of this portion of stress space is closely connected with the mechanical properties of solids. By "realistic stress space of solids", is meant this portion of the stress space. Although some aspects of this problem had been investigated by some authors, there exists even no definite concept regarding the shape, structure and properties of the realistic stress space of solids up to this date.