Although it's possible there could be other reasons, the most common causes for brake lights to stay on continuously include:
burnt fuse ... tail lights are on a different circuit than stop or turn lights
They're on a different circuit. The parking and dash lights go through the headlight switch. It could be the switch, a bad wire/connector or a burned fuse.
check the fuse for the brake lights, they have thier own. also check the brake light switch at the at the top of the brake petal
The running lights have a bad ground.
burnt out lightbulb!
Check the wire which is going inside of the trunk hood to the brake lights.
Blown bulbs, blown fuse, broken or out of adjustment brake light switch.
check the brake light switch on the brake pedal
well if you have allready cheaked the brake fuse it could be that the bulbs have burnt out check that.......As for me we tried to go the easy way with installing a toggle switch and manually turning them off and on, but today the wires melted completely from the battery to the brake lights themself, as of tomorrow we are going to buy a brake light switch and install it. I was told that is what is causing all of this trouble. I hope I helped.
Check the fuses.
check that you have double filament bulbs in tail lights
If you have no brake lights or tail lights then you've probably got an electrical problem. Check the fuses first and see if you have one or more blown.