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A plunger with a simple rubber cup attached to a wooden handle is the best tool for the job. If you have a flange plunger with an extra ring of rubber around the bottom, fold the extra ring into the cup. The plunger will bring up whatever is clogging the drain. Don't use a plunger if you've poured toxic chemicals like bleach down the drain, as it will bring these up, too. They can splash and cause burns. If you have an overflow drain in your tub, this can break the suction created with a plunger. Make sure it is completely closed off by covering it with a wet towel. The outside of the drain may be wet from a recent shower. If it is not evenly wet, pour some water into the tub. Or, use a small amount of petroleum jelly around the edge of the cup of the plunger to get a better seal. If there is a lot of standing water in your tub, remove some of it with a bucket before you start to plunge. This will keep it from splashing you. The cup will seal when you start to pump. Move the handle up and down a few times to force air out. Then push vigorously for about 20 seconds. Don't push so hard that you break the seal. If the plunging worked, it will have brought up whatever was clogging your drain. Remove the clog with your hands or use a wire snake if you can't reach it. Use a flashlight to get a good look. To check that everything has been cleared out, turn on the water and watch to see if it drains. If the water doesn't drain, try using a hand snake or baking soda and vinegar solution.
Use a cup plunger for shower drains if standing water won't drain. Block the overflow drain with a wet towel. Moisten the outside of the drain with water or petroleum jelly if it is dry. Press the plunger around the drain to cover it completely. Start to pump the handle of the plunger gently, and then with more force. Lift up the plunger and remove any material you can reach.