Preheat a grill to high heat.
Cut 4, 12" pieces of foil and 4, 12" pieces of parchment paper. Line up the foil pieces, then place the parchment paper on top.
Evenly divide up the shrimp, andouille sausage, potatoes, and corn and place them on the pieces of parchment paper.
Pour one tablespoon butter or olive oil over the shrimp and veggies in each packet, then season with 1/2 teaspoon Cajun seasoning.
Fold the foil and parchment in half over the shrimp and veggies, then roll up the sides to create a tightly sealed packet.
Place the packs on the grill and cook for 12-15 minutes, until everything is fully cooked through.
Remove from grill, let cool slightly, and serve!