A recently discovered shroud dated at the time of Jesus casts doubt on the Turn Shroud since it has a different weave:

Archaeologists have discovered the first known burial shroud in Jerusalem from the time of Christ’s crucifixion – and say it casts serious doubt on the claimed authenticity of the Turin Shroud.

Ancient shrouds from the period have been found before in the Holy Land, but never in Jerusalem.
Researchers say the weave and design of the shroud discovered in a burial cave near Jerusalem’s Old City are completely different to the Turin Shroud.
Radiocarbon tests and artefacts found in the cave prove almost beyond doubt that it was from the same time of Christ’s death.
It was made with a simple two-way weave – not the twill weave used on the Turin Shroud, which textile experts say was introduced more than 1,000 years after Christ lived.
And instead of being a single sheet like the famous item in Turin, the Jerusalem shroud is made up of several sections, with a separate piece for the head.

Good thing our faith isn’t tied to material proofs like this, huh? 🙂