Tangent shading for BI was introduced in 2.42. According to the [feature note][1]:

> Using the 'tangent' option in the Material → Shaders panel alters the direction of shading to use the tangent vectors, giving anisotropic shading for any of Blender's diffuse and specular shaders. This is useful for creating brushed metal or wood, where the microscopic grooves in the material give highlights that follow a direction, rather than just being circular.

> **Currently, Blender uses a mesh's UV co-ordinates to define the direction of the shading (along the V axis). This means that models must be UV unwrapped to take advantage of tangent shading.**

So, an expected anisotropic result needs UV coordinates to know which direction the light should stretch. To be exact, the anisotropy will stretch the light **vertically along the UV coordinates**.

![enter image description here][2]

For the attached case, You can unwrap it from the side view with UV unwrap methods like Cylinder projection, which is usually recommended. 

  [1]: http://archive.blender.org/development/release-logs/blender-242/material-features/index.html
  [2]: https://i.sstatic.net/I9j5R.png