What kind of wire would i need to carry 20 amps 100 feet underground
Wire size

You can use a calculator like http://wiresizecalculator.net/ to figure this out.

Keep in mind that the distance is not just the distance underground, but the entire wire distance from the panel to the receptacle/switch/fixture. 

For 140', you'll need #6 copper or #4 aluminum.

Burial depth

For a 120V, 20A circuit, protected by GFCI, in residential use, using direct-burial rated wire (UF), the minimum depth requirement is 12".

See also:


What is the best way to run underground electrical and low voltage in the same trench?
How do I run a wire underground to an outdoor post lamp?