As the region struggles with some of the worst weather in living memory, an Austrian army spokesman said the avalanche had struck the ski resort of Galtur in Tirol. Continuing heavy snow was hampering rescue efforts.
There are several dozen British families staying in Galtur, but there were no immediate reports of casualties among them.
Chris Laming, a businessman from Kent on holiday in Galtur with his wife and two children, was in the villagewhen the avalanche struck. He said it "obliterated" a hotel full of tourists and several chalets on the edge of the village. A Dutch holidaymaker recovered five bodies from the avalanche.
"The avalanche didn't hit us directly but it was the weirdest thing I've ever experienced. We had all been taking part in a makeshift skiing competition, organised by the tourist office, in the centre of the village.
"We had just gone back inside the hotel room when suddenly everything went black. There was no sound at all, and then something smacked against the window like a giant shockwave. Then you heard it hitting the other side of the hotel."
An Austrian army major said the 35 missing people were believed to be trapped in houses and the hotel buried beneath the snow.
The major said people trapped in homes have a better chance of surviving and finding air pockets than those caught in the open, where the heavy weight of the snow soon suffocates them.
Many tourists were walking down the main street with their children to join a village party organised by the local authorities when Galtur was engulfed.
No outsiders have been able to reach the village since snow last week blocked the main road leading there, and bad weather prevented helicopters from flying from the town of Landeck lower down the valley.
Mr Laming told The Independent by phone last night: "We rushed downstairs to find crowds of people coming into the hotel in great distress, and children crying. A German man was screaming two names, presumably those of his children. A little British boy had gone missing but he was found unharmed outside a few minutes later.
"Outside it was still daytime but almost black. We didn't realise at the time the real action had taken place on the edge of the village a few hundred yards away, and that it was much worse over there. Everything was covered in powder snow and a thick fog.
"Some people went to the scene with the police immediately to help with the rescue.
"Now people are very upset and very scared. We do believe we are safe because our hotel is in the middle of the village, away from the slopes, we're probably about 300 to 400 metres from where it happened.
"They are evacuating people from the edge of town and putting them up in the hotel. Now it seems conditions are getting worse, there's a gale blowing."
The Alps are experiencing their worst weather in 40 years. More than 20 people - including six Britons - have died in avalanches this season. Even areas traditionally considered safe have been affected.
Tens of thousands of skiers, including many British tourists, are trapped in heavy snow affecting the Alpine region. Main routes are blocked by snow and resorts and villages marooned. Avalanche alerts rate five on a scale of five. The extreme western reaches of Austria are among the worst affected areas.
Hans-Jorg Pacher, spokesman for the Tirol tourist board in Innsbruck, said between 12 and 15 ski resorts are cut off, as well as dozens of smaller villages. The resorts include Lech, where Diana, Princess of Wales holidayed with Princes Harry and William, St Anton, and Zurs, a tiny hamlet favoured by the German aristocracy.
Switzerland, Italy, France, Austria and Germany have mobilised their armed forces to fly in supplies and help with emergency airlifts. In the Swiss canton of Valais, officials recorded an avalanche every 20 minutes on Monday. Metres of snow have fallen.
Every country that shares the Alps has been hit by tragedy. Yesterday a 52-year-old woman died in Morgex, Italy, near Mount Blanc, after a wall of snow, 300 metres wide, pounded the village in the early hours of the morning. The woman was asleep when the snow ripped through her home, removing the roof and crushing her against the wall.
No one else died although 50 houses were damaged and three villagers were injured.
While Italian rescue workers struggled on, about 100 Swiss rescue workers were still trying to recover eight French tourists buried in an avalanche at the weekend in the village of Evolene, in Valais canton. Yesterday officials in the village warned that the chances of finding them alive were very slim. Among the missing are a baby and a small boy.
On Sunday the bodies of two local victims - a 23-year-old council employee and his girlfriend, aged 22 - were recovered from beneath the snow. If, as is now expected, the French tourists are dead, Evolene will enter the history books as the site of the most lethal mountain accident to have hit Switzerland in 14 years.
In Austria avalanches are occurring in some areas for the first time in living memory. Such was the case in the village of Gargellen in the western Vorarlberg province, where an avalanche destroyed a mountain restaurant on Monday. Five ski-lift employees and five workers on the restaurant's lower floors survived, but a couple in the attic of the building died.
A woman perished immediately and her male companion died later from injuries after weather conditions prevented him being flown to hospital.
Snowstorms, blizzards and the risk of avalanche were also preventing rescue parties searching for three French skiers stranded for the seventh day above the resort of Pralognan-la-Vanoise in the French Alps.
The three men were in mobile phone contact with local police until Sunday night, but that link has been lost. The men had said they were sheltering in an igloo but were running out of food and water, and struggling against bitter cold.Reuse content