I was able to do so, but those buttons gone (probably compatability with new hardware issue) , but anyway I need some workaround - shortcut or using a menu bar. How I was doing it in the past: I selected some area, then Move Tool and then there buttons appeared (under all tools icons): button for moving selected pixels, button for moving shape of selection itself (contour)...
If your move tool happens to be in "move layer" mode or "move path" mode, hold Alt as you drag. Then the active selection moves.
In the general case, you use the Move tool, in "Move selection" mode (red square icon in the "Move" line in the Tool options), to move the selection mask.
The Rectangle and Ellipse selection can be moved directly while in the selection tool by clicking inside and dragging.
See here for additional information.