Clear the area around both openings of your culvert using a shovel. Dig out any sticks, sand, gravel or other debris that might be blocking the entrance and exit of your culvert. Place this debris and gravel in a wheelbarrow, so it can be removed from the area and reduce the risk of the same debris blocking your culvert again in the future.
Stick your shovel as far into the culvert as possible and drag it toward you, pulling out gravel which is lining the bottom of the culvert. Continue doing this, from both ends of the culvert until you feel you're unable to remove any more gravel using this method.
Take a power washer and aim the nozel into the culvert. This sudden flow of water should work to push any small gravel pieces that were left out the other side of the culvert. Continue doing this until you have removed as much gravel as possible.
Clear out the entrance and exit of the culvert again using your shovel, as more debris may have accumulated as a result of the power washing. Place any debris removed into the wheelbarrow and dispose of it far away from the culvert.