Cut cardboard into an elephant-shaped outline. Use an image of an elephant as a guide if necessary. The outline should be a profile with a body, head, trunk, tusks and two of the four legs.
Cut a second cardboard silhouette of the same elephant with the other two legs in the positions you want the final model's legs to hold. The model should have at least three points of contact with the ground.
Stuff small plastic bags with crumpled newspaper and tape them shut, then tape the stuffed bags between the cardboard silhouettes to bulk out a 3 dimensional model of the elephant.
Tape additional bags onto the outsides of the silhouettes, using your hands to crumple each bag into the desired shape, until the overall shape roughly matches the look you want your lawn decoration to have. If desired, wrap the entire model in plastic packing tape to even out the surface and create an extra layer of internal waterproofing.
Cut elephant ears out of card stock and tape them to the model's head in the desired position.
Mix equal parts flour and water to create papier mache paste. Dip torn pieces of newspaper into the paste and layer them onto the model. Continue adding layers until the model has the desired shape and texture, allowing the papier mache to dry completely after every 3 to 4 layers.
Paint the model with the desired colors or patterns. For a realistic elephant, use gray paint with a darker tone to emphasize or simulate wrinkles, and white and black for the eyes. Paint more whimsical yard elephants with bright colors, flowers or other patterns on them. Allow the paint to dry completely.
Paint the elephant with two to three coats of boat varnish, allowing the varnish to dry completely between coats. Ensure to paint every part of the surface, especially the bottom.