In the current month of Elul, it behooves us to try and observe the Mitzvot more carefully and to be more cautious not to violate any transgressions. It is therefore worthwhile to clarify one area of Shabbat observance that many may are not be aware of.
There are 39 acts that are prohibited, one of them being Mehatech, or cutting for a creative purpose. If someone were to rip open a potato chip bag, for example, this would be permitted because the cutting is destructive in nature and because one is not doing so for the sake of cutting, but rather to access the food inside. If one cuts paper for a constructive purpose, however, the Mishna Berura (O.H. 340:41) explains that one would be liable for both acts of Kore’a (tearing) and Mechatech. Thus, cutting aluminum foil or plastic wrap is not permitted on Shabbat, and certainly not cutting precise sizes or shapes so as to properly cover food.
Summary: One may tear open bags or wrappers on Shabbat for the purpose of eating food. Tearing aluminum foil, plastic wrap and the like are not permitted on Shabbat.