By Dave Graham

CRANS-MONTANA, Switzerland, Jan 4 (Reuters) - Hundreds of people silently filed through the frosty streets of the Swiss ski resort of Crans-Montana on Sunday to remember victims of a New Year bar fire that killed at least 40 people and injured more than a hundred others.

Following a packed church mass that spilled outdoors, the crowd slowly walked towards an impromptu shrine to the victims next to the "Le Constellation" bar that went up in flames in the early hours of January 1.

"It's to be together with the people who are suffering, who have lost somebody in the family, children or friends," said 76-year-old Charlotte Schumacher, a participant in the procession. "I know people who have lost their grandchildren."

Teenagers as young as 14 or 15 years old were among the dead, and the severity of the burns suffered by the victims has made the process of identifying them difficult.

Attendees of the interconfessional church service hugged and shook hands as the prosperous Alpine town sought to pull together to process the trauma of one of the deadliest tragedies to strike modern Switzerland.

Prosecutors said the fire was likely caused by sparkling candles igniting the ceiling of its basement. Swiss authorities have put the two people who ran the bar under investigation on suspicion of crimes including homicide by negligence.

The injured and missing came from all corners of Europe and as far afield as Australia, underlining the international appeal of the picturesque resort with panoramic views of the Alps.

But most of the tally were Swiss. The toll might have been worse if emergency services had not acted so quickly, residents said.

"Within minutes you had ambulances; within minutes you had the police that did their job and they did it unbelievably well," said Max Haus, a local business owner who witnessed the harrowing aftermath of the blaze.

As Sunday's sombre procession reached its conclusion, applause began rippling from one end to the other as dozens of police and emergency services workers, some of them in tears, came up through the middle to be celebrated as heroes.

"It's unimaginable what they did, what they have seen," Bruno Huggler, the director of tourism for Crans-Montana, said of the rescue workers. "And now it's very important to take care of them."

(Reporting by Dave GrahamEditing by Christina Fincher)