Abstract: Sandstone and limestone specimens were carried out on uniaxial compression tests, and the similarities among stress-strain curves were remarkable except peak strength and elastic modulus. Further tests on artificial solid materials, including gypsum, concrete and ginger nut cemented with quartz sands, showed striking similarity and tendency in stress-strain curves. General summery of those sigmoid curves contained three curves and connected by two inflection points. The results indicated strong universal regularity for solid material under uniaxial compression test. This regularity has significant guidance to evaluation and prediction of deformation and failure process on geological engineering.