The work studies regularities of the formation of wedge-shaped twins under growing concentrated load in single crystals of bismuth, zinc and bismuth-antimony alloy. It was established that the twinning, detwinning and stopping of the twin deformation near the stress concentrator can take place simultaneously with the load growth. Reversibility of plastic deformation during twinning in metals at the stage of residual twinning development were discovered. Various manifestations of spontaneous detwinning of wedge-shaped twins which emerge at stress concentrators when indenting Bi, Zn, Bi-Sb single crystals with increasing load are quantitatively studied. Depending on the value and the sign, local fields of elastic stress can encourage or discourage twinning, or cause detwinning.