Hi Serge,
In texture mode rotate the texture so that its Z axis is vertical. The axis of the rings is the Z axis of the texture, so in order for the rings to appear properly the Z axis of the texture needs to align with the Y axis of the stump.

From the Help menu (If you’re not familiar with accessing the Help menu, rt. click on “Annual Rings” in the shader properties and select “Show Help”) :
Annual Rings
If enabled, the Wood shader will display growth rings that are arranged in concentric rings around the growth axis. This axis is the texture’s blue Z axis (main menu: Tools | Modes | Texture Axis. Move or rotate this axis if the growth rings should lie differently on the given object.