If you are building a competition model that is going to put a lot of stress on the recovery device (generally a parachute) when it deploys due to the weight of the rocket and/or its payload or the potential velocity at opening, then a standard plastic model rocket parachute with shroud lines held on at the corners with tape discs will not work. Generally, it is Eggloft rockets that put this kind of stress on a parachute, although some larger Super-Rocs or Payload models, or Plastic Model conversions, can do it as well. In these cases the shroud lines either rip out of the tape that is holding them on, or the plastic itself rips from the stress of the opening shock.
Your choices for stronger parachutes are to either go to a cloth chute of some type (generally nylon, sometimes even ripstop nylon) with sewed-on shroud lines, or to build the plastic parachute in a different way. Nylon parachutes are more expensive than plastic, weigh more, and do not fit as much parachute area into the same packed volume, but for higher power-class Eggloft Altitude models where these factors are not important to performance they are probably the best choice.
Another approach is to make your plastic parachute in a different way. This is called “over the top” shroud lines. It can be used with thin parachute material such as 1/2 mil Mylar or drop cloths for single-egg Eggloft Duration in lower power classes, or it can be used with thicker plastic such as garbage bags for heavier rockets. For these parachutes, the shroud lines start at the anchor point to the rocket and run up to the canopy as usual, but then they keep going as one continuous length over the top of the canopy through its center, and down the other side back to the anchor point. This way the force of the parachute’s opening is borne entirely by the shroud lines, not by the fragile canopy material or weak tape discs. In order to keep “over the top” shroud lines in place and to keep them from tangling, it is necessary to tack them down to the canopy at both edges, at the center, and (for larger chutes) at spots between the center and the edges. In fact, many people just run a long strip of narrow Mylar tape along the whole length of that part of the shroud line that is in contact with the canopy. It is important when doing this to use a kind of tape whose adhesive does not get gooey and runny in the sunlight; masking tape will not work. And it is important to powder the whole canopy with rubbed-in baby powder to cover any areas of exposed tape or adhesive that might cause parts of the canopy to stick to itself and prevent full opening.