If a shower drains sluggishly, try filling the base with an inch of water and plunging. If the clogged shower drain does not respond to plunging, remove the strainer and attempt to clear the blockage with the two methods shown here. Begin by prying up the strainer with a screwdriver. (Some strainers may have a center screw. Remove it, then pry up.)
Try to Auger or snake through the Strainer
Push an auger down the drain and through the trap. Push and pull to remove a soap clog. If the auger hits a blockage, pull out the auger. The blockage may come with it. If it doesn't, push the auger to try to force the clog into a larger pipe.

A Hose might Unclog the Shower
If plunging doesn't work, thread in an auger. The tub will have a stopper or a trip-lever assembly like the one above. Pry up or unscrew the strainer to insert the auger/snake. This method will reach only to the tee fitting. If the clog is farther down, you'll have to go through the overflow tube.
