Step 1: U Lock
Insert a u-lock through your bike rack so the open end of the lock is above the rack and the closed end goes below but hits a leg of the rack or some part of the rack that stops it from going all the way through. This only works on some racks. Attaching a plank of wood across the rack can also work if you don't have a u-lock.
Step 2: Hanging the Case
Slide the u-lock through the handle of the briefcase and lock it.
Step 3: Secure the Case
Secure the briefcase with bungees or used bike inner-tube or both. It is best if the bungees or inner-tube help pull the case up to reduce the stress on the handle.
Step 4: Test for Looseness
Make sure it will not fall off by lifting and pulling on the case.
Step 5: Test the Placement
The briefcase may hit you foot as you pedal, which is the most common problem with this strapping method. The bottom of the case is the part that hits your foot, so raising back case will help. Push it back as far as possible and use the straps to keep it off your heal. Sliding something under the back side of the u-lock can help too.