With all the wear a Craftsman lawn mower's tires receive every season, it is no wonder the occasional flat occurs. Sometime the smallest things create a puncture in the tire, allowing the air to quickly escape. Tire repair fillers--such as flat fixer and foam fill--may not get the job done. Remove the wheel entirely and take it in for repair, or just replace it with a new one.
Park the lawn mower in a flat, level, hard surface area. A concrete driveway or walkway is ideal--preferably in the shade.
Set the mower's parking brake and chock the front wheels with a large board. Since the back of the mower is going to be jacked up, place the chocks in front of the wheels.
Locate a couple of large blocks to set the rear of the mower on. Cinder blocks or pieces of scrap wood will work, as long as they are large enough to keep the rear tires off the ground.
Jack the rear of the mower up until both back tires are off the ground. Use a car or floor jack. Slide the blocks under each end of the axles, a few inches to the inside of each rear wheel. Release the jack and set the rear of the mower down onto the blocks. Wiggle the mower to make sure sits securely on the blocks.
Remove the dust cover from the outside-center of the wheel. Gently pry the platic cover off with a flat-head screwdriver. Place the tip of the screwdriver along the edge of the cover. Once the cover begins to separate from the wheel, pull it free and set it aside.
Snap off the half-moon key retainer holding the wheel onto the axle. The key wraps halfway around the axle, and sets in a recess cut into the shaft. Insert the flat-head screwdriver into the top half of the key retainer and twist the screwdriver as if removing a screw. The key will separate from the shaft.
Grasp the rear tire and wheel with both hands at the nine and three o'clock position. Slightly wiggle the tire while pulling it away from the mower. The tire and wheel slide off the axle and key-stock.
Tape the square key-stock onto the shaft. The key-stock is visible once the wheel is off. It mates with a groove cut into the inside diameter of the wheel, and prevents the wheel from spinning on the shaft. Taping the key-stock in place prevents losing it before the new wheel installation.