Three people have died and at least eight more were missing on Sunday as torrential rains lashed central Europe, triggering floods and landslides, disrupting transport and forcing hundreds to evacuate.

Austria, Germany and the Czech Republic sent in army units to help with rescue efforts after rains reached record levels in some areas, while hundreds of roads have been closed and rail services cut.

The banks of the mighty Danube river burst in one area in Germany while dozens of towns have been put on flood alert across a large swathe of central Europe.

In Austria, one person was killed and two were reported missing following landslides triggered by heavy rains that forced several hundred people from their homes, local authorities said.

Two people were also missing in neighbouring Germany following a 48-hour downpour that hit record levels in parts of the south and east, according to the DPA news agency.

But despite the heavy rains, around 10,000 Bayern Munich fans joined in celebrations for their team's historic treble win in the European, league and cup titles.

In the Czech Republic, a man and woman were killed in Trebenice, just south of Prague, when their house collapsed. At least four other people were missing.

The government declared a state of emergency and released 300 million korunas (12 million euros, $15 million) in disaster funds. Several hundred people had to be evacuated, as well as a hospital and the Prague zoo.

"We will do everything to protect people's lives and health," said Prime Minister Petr Necas, announcing that 1,000 troops had been mobilised.

"Tonight and tomorrow will be critical," he said.

Barriers have been erected along the banks of the Vltava river in Prague to prevent it from flooding, and the iconic Charles bridge was closed.

German Chancellor Angela Merkel pledged federal government support for the affected areas, while the army was sent in to help in some towns in the east as water levels rose.

The southern German town of Passau on the Austrian border was partly flooded when the Danube burst its banks.

Further downstream, Austrian towns including Linz and Melk were bracing for the worst, with some local authorities fearing a repeat of the record floods in 2002 that caused damage of up to 7.5 billion euros nationwide.

Rail services between the southern German city of Munich and Salzburg in Austria were brought to a halt.

In Austria, much of the western provinces of Vorarlberg, Tyrol and Salzburg, as well as northern Upper Austria, were on flood alert.

Rail links were suspended due to landslides in many parts of Salzburg and Tyrol, Austrian Rail said, while a section of the motorway to Switzerland was closed because of flooding, as were smaller roads throughout the country.

In a small town near Salzburg, a worker helping with the clean-up effort was killed in a landslide on Sunday, police said.

In nearby Taxenbach, rescue services were still searching for two people -- a farmer and a female driver -- believed to have been caught in a mudslide overnight.

Hundreds of firefighters and emergency workers, as well as the Austrian army, have been mobilised to help clear roads, assist with evacuations and put up anti-flood barriers.

At least 240 residents in Salzburg and another 80 in neighbouring Tyrol were evacuated from their homes as local rivers threatened to burst their banks, local authorities said.

Open-air music festivals and other events were relocated or partly cancelled as a result of the weather.

On Saturday alone, Vorarlberg province saw up to 132 millimetres (about five inches) of rain, according to the Austrian meteorological centre ZAMG.

In just a few days, Austria has experienced as much rain as it normally would in two months during this season, ZAMG added.

In Switzerland, the federal weather office said water levels were still rising in a number of lakes and there remained a risk of landslides although in general the situation was under control.

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