The Eevee render engine doesn't currently support the Anisotropic node, but there is a way to simulate it with a simple node setup. Here's a summary.

1 Node Setup for Simulating Anisotropy

Eevee is insanely fast – well, it has to be, being supposed to be real-time. But that's because it cuts all sorts of corners at the cost of realism. Yet it's sufficiently versatile to address all the needs. The following node setup will do the business of simulating anisotropy. The two essential parameters are the colours of the MixRGB node, typically both the same hue but with different values, the first one being that of the metal, the second one that of the light hitting it.

Nothing keeps you from adjusting the Metallic and Roughness values of the Principled BSDF node – I've seen people even touch the Specular level – but none of this is necessary. You can adjust the IOR of the Fresnel node to change the thickness of the effect, but most people prefer squeezing in a Gamma node between the Fresnel and the MixRGB nodes, which I didn't bother doing in this simplest of examples.

One aspect I still don't understand, is how to control where the light converges to. In particular, if you model a vessel from a curve you apply the Screw modifier to, it will converge to a seemingly random point I couldn't for the life of me adjust. However, note that converting it to a mesh will make light converge to its centre, which is probably what you want

2 References

• Blender 2.80: Eevee lists what shaders the engine supports or not.
• Blender 2.8 Eevee Anisotropic Shader Tutorial
• Fake Anisotropic In Blender Eevee