Cats enrich our lives in many wonderful ways. But when a cat stops using the litter box, the frustration can overshadow even the most wonderful parts of the person-pet relationship. There are several reasons a cat may start going outside of the litter box. Begin by ensuring you are doing your part to encourage the cat to use the litter box. If all is well on that front, your next step is determining the cause of the problem.
If you've ruled out slip-ups on your part as well as medical or territorial (marking) causes, you likely have a behavioral issue. Often, a cat may stray from the litter box if he finds another area that he prefers, or if the setup of the current box that isn't working out for him. Your job is to convince your cat that other areas are not desirable and that his box is the best of the best.
To begin, notice where your cat eliminates. Is he drawn to particular surfaces, such as the bathtub or nylon bags? Remove the temptation by either limiting his access to these areas or removing these items. If just closing doors to keep the cat away from appealing areas isn't possible, make the area less inviting to the cat. Generally cats don't like the smell of citrus, so leaving oranges nearby or using a pet-safe citrus cleaner can act as a deterrent. Cats also don't like the feel of double-stick tape on their paws. Laying down a perimeter of tape can create a barrier most cats won't want to cross. Keep in mind that most of these measures are only temporarily necessary. Once the cat returns to the box and uses it consistently, you can begin phasing out these measures.
Your other challenge is to make the litter box appealing. Scoop and clean it religiously. Be sure the box is easy to get to--cats aren't usually interested in navigating their way through a cluttered basement to locate a box in the very back corner. Or perhaps your cat is trying to tell you something about the box itself. The best way to learn what your cat wants in a box is to offer two boxes, side by side. Then, change one variable. Use clumping litter in one and clay in the other. See which your cat uses. Try the same thing with covered and uncovered boxes. Your cat will show you what setup works best for him. Remember to vary just one item at a time so you can be sure you are honing in on your cat's preferences. You may notice that your cat prefers to urinate in one box and defecate in the other. If so, keep two boxes side by side to allow for that.
Very quickly, you should see what works best for your cat. And when the cat is satisfied with the box and using it appropriately, everyone feels better.