The paper considersin terms of modeling and experimental testingthe softening stage manifested in structurally inhomogeneous materials under quasi-static and cyclic load. The method which is used to build the theoretical basis is typical for mechanics. It starts with defining a new material propertystrain-softening phase. The stage is realized in the form of a descending branch of the curve on computer diagrams recorded during simple tension or torsion tests on non-reusable specimens in a

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... ably rigid testing machine. The type of such a diagram is determined by the structural inhomogeneity of a material, which is defined by distribution law for strength and plasticity properties of structural elements. Complete stressstrain curves or diagrams (CSSD) with a branch descending to zero have been plotted for materials of various classes. Degradation of parameters of a descending branch on a computer diagram recorded for trained specimens provides a new angle on the subject of relation between static and cyclic material properties. The experiments and modeling which were carried out provide basic understanding of softening in terms of deformation.