How can I make an endless 3D moving background?

I have started to work on a top-down bullet hell game with 3D models and I wanted to make a fast moving 3D background under it. It would be a concept pretty similar to Ikaruga in terms of the background running under it. I have found plenty information about 2D parallax scrolling, but it hasn’t work all that well on 3D for me. I have used as reference for learning the Unity3D Top-Down Shooter tutorial from the English website and the Top-Down Shooter tutorial from the Japanese webpage.

Any information or material for learning would be appreciated.

You could have a simple plane underneath the main play area which moves with the camera. To simulate the camera’s motion, you an make the texture on the plane scroll by changing it’s UV values. Here is some code from an old UV Scrolling script from an early project of mine:

private Vector2 uvOffset = Vector2.zero;
public Vector2 uvAnimationRate = new Vector2(0.0f, 1.0f);
int materialIndex = 0;
string textureName = "_MainTex";
private Renderer renderer;

void Start() {
     renderer = GetComponent<Renderer>();
}

void Update () {
    uvOffset += ( uvAnimationRate * Time.deltaTime );
    if(renderer.enabled)
    {
    	renderer.materials[materialIndex].SetTextureOffset(textureName, uvOffset );
    }
}