How did the schlieffen plan help cause stalemate?

The Schlieffen Plan itself did not lead to stalemate; indeed, if the French were unprepared, the plan might have worked. The stalemate was caused by: very efficent railways quickly getting troops to the front; advanced (for their time) machine-guns causing soldiers to dig in to escape enemy fire; armies on both sides with comparable resources and numbers; and old-style battle tactics (e.g. charge the enemy lines--what, didn't that work?--well, charge again...) which were not flexible enough to cope with the new style of war. This is just a brief overview. Others may have more to offer.