In situations where the presence of beaver is inappropriate or the landowner wishes to control numbers on his property, removal by live trapping outside the breeding season is the most effective solution.  

A Hancock Trap literally scoops beaver alive out of the water for relocation.
[Sherri Tippie and Jerda Smeltzer]

Ideal for catching beaver unharmed are 'suitcase traps', such as Hancock live traps.   The trap looks like a large suitcase and will spring closed when activated.

It can be used in feeding areas and is baited with lures, such as poplar oil, fresh split aspen twigs or castoreum .