Creating an elephant costume featuring a distinctive trunk can be as simple or as complicated as you want it to be. An elephant costume is composed of three parts: a body, a mask, and a trunk. In many ways, the trunk is the most important part of the costume, as it serves almost singlehandedly (along with the mask's requisite large ears) to distinguish the costume's identity from other gray animals. Focusing your energy on the trunk will make sure your elephant costume stands out.
Create the elephant costume body using a gray sweat suit or gray sheet. With a sweat suit, simply clothe yourself in gray, adding, if desired, detail touches like a small tail with a "brush" on the end and gray socks featuring large, painted-on nails. You might also want to pad your costume using pillows. A gray sheet, pinned around the neck or with a hole cut for the head to fit through, can serve equally well to represent an elephant's bulky body.
Create an elephant mask. A simple mask can be made from paper; secure a strip of paper around the head, then attach floppy paper ears, cut to mimic an elephant's. For a more durable (but time-consuming) project, create and elephant mask out of felt. Cut eye-holes and emphasize the elephant's floppy ears.
Create the elephant trunk to attach to the mask. For a quick costume, a long strip of paper, flared at the end to mimic the elephant's agile, finger- or lip-like trunk ends, will do the trick. For a 3-dimensional rendering, attach tubing, such as several taped-together paper towel roll cores, painted gray and attached to the mask or around the head using an elastic band. For further detail, attach "tusks" made of paper or white-painted toilet paper roll cores to flare out on either side of the trunk.