The mechanical conditions under which solids can deform permanently without fracturing are of interest to engineers, metallurgists, and, in some applications, to geologists. The ductile metals are the most widely used artificial materials of construction. It is natural, therefore, that their mechanical properties have been widely investigated by engineers and metallurgists. Among these metals soft steel shows the peculiarity that when it is deformed to a small degree fine markings of an astonishingly regular pattern appear on the surface of the deformed test‐piece. These fine patterns frequently accompany the first plastic deformations after the yield‐point has been reached in steel. They are traces of thin layers in which the metal has been deformed locally. The description and geometry of these surfaces of slip has opened up broad theoretical approaches to a mechanics of the plastic states of stress in steel. In minerals and in rocks, on the other hand, many evidences of permanent deformation are known to the geologist. A description of the plastic distortion observable in the strata of rocks is one of the fundamental problems of geology. The conditions encountered in the deeper sedimentary or igneous rocks—the prevailing of small differences of stress, of elevated temperatures increasing with the depth, of high average pressures—are important factors contributing to plastic flow. Changes in the structure of rocks are known which are frequently very similar to those which have been observed in plastically deformed metals. A number of observations of this kind were shown in examples of which a large number have not been yet reported in publications. The flow‐patterns were demonstrated in the following examples: Compression of prismatic steel pieces; compression of paraffin cylinders; flow‐lines starting near a small hole in bodies deformed by compression; a case of this type in meteoric iron. In an extruded tube of clay beautiful markings were discovered through an accidental fracture of the tube, disclosing the flow‐pattern in the tube wall which had been influenced through the friction along the tube surface. Square and rectangular plates were deformed by means of a concentrated load while the plates were resting along their circumference. Again beautiful very regular flow‐patterns appeared on the surface of these plates. If a steel block, the surface of which has been polished, is deformed by a concentrated pressure, for example, if the pressure is exerted by means of a cylindrical punch, beautiful slip‐lines appear around the impression consisting of two systems of logarithmic spirals. Reference was made to observations in Japan in which it was claimed that the secondary cones on one of the volcanoes in Japan appear to be distributed along similar logarithmic spirals which would indicate a radial symmetry of the stress‐field. In a motion‐picture film several examples of the propagation of the plastic zone and of the formation of surfaces of slip were demonstrated in tension‐tests and in bending tests with plates.