The last papal viewing of the bloodstained cloth was by Benedict's popular predecessor Pope John Paul II in 2000.
The Polish pope encouraged scientists to continue their analyses, "to reach adequate answers to the questions connected to this Shroud" while respecting the "sensitivity of the faithful."
Some two million people are expected to view one of the most revered objects in Christendom - and among the most disputed - over six weeks that began on April 10 in this northern Italian city.
The showing is the first time in a decade and the first time since the shroud was painstakingly restored in 2002, with the removal of patches and a backing cloth that were added after a fire damaged it in 1532.
While millions believe the shroud to be authentic, sceptics believe it is a medieval fake.
A section missing from the upper right-hand corner of the fabric was used for radiocarbon dating analysis in 1988, when samples were sent to four different labs.
Although the analysis determined that the fibres in the cloth date from the Middle Ages, sometime between 1260 and 1390, those findings have in turn been challenged with suggestions that the samples were contaminated.
New technologies have offered ever new ways to analyse the shroud.
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