Either. Probably will snake through the shower drain.

Why would they snake through the shower drain, when it clearly isn't the problem, and can accommodate only a small snake?

Warning about cost: Around here, at least, there's a high minimum charge for a "sewer machine" (a snake big enough to clean out a main sewer line). I would call a trusted plumber first, to determine where the clog is. If they can see enough of your piping, they can figure out whether the clog is in the house or in the main line.

(i>Why would they snake through the shower drain? The clog is clearly downstream of the shower drain and maybe the merge of any associated branch lines (hence the backup) so it's logical to access it that way first. Pull up the strainer, get to it, and see what happens.

If that doesn't work, next step might be clearing a bit lower, or the main drain itself.

The horizontal section of pipe after the sanitary tee for the shower drain is one of the most common places to have a drain clog. The other place is the same section of pipe after the washing machine standpipe.

Why are these such common places to have a blockage?

Because these have a 2" P-trap. The P trap is like the clog factory. That is where the clogs start out. When the clog gets dislodged from the P-trap, it flows down the trap arm and past the sanitary tee. When you plunge a clogged drain, you are forcing the clog down to the sanitary tee. Once it passes the sanitary tee, the plunger is ineffective, because the vent breaks the vacuum created by the plunger.

If the P-trap and trap arm are 1 1/2" pipes, and the sanitary tee steps up to a 2" pipe, the 1 1/2"clog can flow freely through the 2" pipe. But if the clog comes from a 2" P-trap, it will most likely get stuck further down the line in the next horizontal section of 2" pipe.

Once a clog gets past the sanitary tee, plunging is futile. You must snake out the clogged section of pipe.

So the reason to start with the shower drain is because the clog is most likely in the 2" pipe, not a larger one.

I could see that, if the problem was the drain backing up when using the basement shower. But the original post seems to say otherwise -- water used elsewhere in the house is coming up out of the basement shower drain. Not sure whether that includes toilets. I'd think that toilet waste backing up into the basement would merit special mention :-(

"the vent breaks the vacuum created by the plunger. "

that is not how a plunger works.

It is forcing water into the line to move the clog.

After a vent comes off all the water does is rise up in the vent.

Brick,

Not to argue semantics, but "vacuum" is the right word to describe how the plunger can force water into the line to move the clog. The plunger will not work unless the rubber cup makes a seal around the drain, and that is technically making a vacuum.

Here is a textbook definition of how a plunger works:

The plunger is inserted into the bowl of the toilet by holding the wooden stick and setting the rubber cup over the bottom drain of the toilet. The flange underneath the plunger cup will fit into the pipe, and the cup overlaps the outer edge of the drain to create a seal. The plunger stick is then pushed down, inverting the rubber plunger cap and forcing the air that was in the plunger cap into the pipe. The plunger is then pulled back, sucking air and water up with it, causing a vacuum. This abrupt force of air and water pressure helps loosen a clog in the pipes and gets the toilet pipes draining again. It may take several repeated motions of pushing and pulling back on the plunger to loosen the clog.

Read more: How Does a Toilet Plunger Work? : eHow.com http://www.ehow.com/how-does_4759289_toilet-plunger-work.html#ixzz1J412KFbm