Here is a story from strategypage.com.
Basically it states that shoulder fired missles might damage, but will not bring down a modern, large Jetliner. Older models are vulnerable.
"Larger airliners, like the Airbus's, and 757s, 767s and 747s, have not been brought down because these missiles were not designed to take on aircraft with such large and powerful engines. While these missiles were originally intended for use against jet fighters operating over the battlefield, the reality turned out to be different. The most likely targets encountered were helicopters, or propeller driven transports. These aircraft proved to be just the sort of thing twenty pound missiles with 2-3 pound warheads could destroy. Against jet fighters with powerful engines, the missiles caused some damage to the tailpipe, but usually failed to bring down the jet. This was first noted during the 1973 Arab-Israeli war, where the Egyptians fired hundreds of SA-7s at Israeli A-4 light bombers. Most of the A-4s, with their 11,187 pounds of thrust engines, survived the encounter. Larger jets, like the F-4 and it's 17,000 pound thrust engines, were even more difficult to bring down. Smaller commercial jets, like the 737 or DC-9 (each using two 14,000 pounds of thrust engines) have proved vulnerable. But a 757 has much larger engines with 43,000 pounds of thrust, and the 747 is 63,000. Moreover, the rear end of jet engines are built to take a lot of punishment from all that hot exhaust spewing out. Put a bird into the front of the engine and you can do some real damage. But these missiles home in on heat, and all of that is at the rear end of the engine."
Quilly Mammoth