Can I run a 50 amp circuit underground?
Cable
The cable you're looking for is Type UF, or Underground Feeder cable.

It can be purchased at big orange, and big blue, by the foot. It's available in 6/2, 6/2 with ground, 6/3, and 6/3 with ground, and is rated for direct burial.
Attachment to Service
There is one temporary, and two permanent ways to supply power to a park trailer.
Temporary
Power-Supply Cord
You'll want to use a NEMA 14-50 receptacle, and 4 wire cord with NEMA 14-50 plug to connect the trailer to the service.  The trailer's electrical grounding will be through the service plug, so only the distribution panel will have to be grounded.

Permanent
Mast Weatherhead
You can use four continuously insulated, color-coded feeder conductors strung from a mast to a weatherhead as a permanent feeder.

Raceway
A metal raceway, rigid nonmetallic conduit, or liquidtight flexible nonmetallic conduit, from the disconnecting means to a junction box on the underside of the trailer can serve as a pathway to run permanently attached feeders.

NEC
For reference, park trailers are covered in article 552 of the National Electrical Code.