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If you're only running cold water to your shower, chances are good you won't be spending hours getting wet. As such, drainage should not be a major concern. Still, you need some layer between your feet and the ground, otherwise you'll end up with dirty, muddy feet after every shower. Gravel is by far the most common bottom for outdoor showers. It is easy to install, looks good, and naturally drains away water if you take shorter showers. You can buy gravel, river pebbles, or small stone mixes depending on your aesthetic desires. To effectively install a gravel floor:  Smooth out the flooring the best you can. Lay down your stones around the shower. For a more professional look, use half-buried 2x4s to create a simple enclosure around your shower that will hold the gravel in. Use a tamper to press the gravel tightly together, leaving you with a smooth, regular floor. You'll need one 8-foot 4x4" piece of wood and one 8-foot 1x4" piece, both pressure treated. You'll use the first piece to build a square base for your floor, and the second piece to put together the drainable flooring. For a cheap, pre-made alternative, consider using a wooden pallet.  Cut one of the 4x4's into 4 even pieces, then screw them together into a simple square frame. Cut a 1x4" into 7 individual pieces, each 26-1/2" long. Place your 7 pieces onto your board starting on the edge, each piece parallel to the next. Leave a 1/4" space between each board for water to drain through. Screw the floorboards into the wooden frame. The easiest way to make a shower wall is to set up four more posts (identical to the one holding up your piping) in the ground, then nail plywood sheets to the posts as walls. You can then attach decorative shingles, paint or stain the plywood, or add a door/curtain instead of wood for one of the sides. You can get a set of outdoor shower walls from a variety of places, and there are a lot of different sets out there that can make your life much easier. However, these sets can run up to $1,000, so it may be more cost-effective to build your own walls instead. This strategy, of course, only works if your shower is attached to a wall or fence. That said, a simple curved shower rod can cover up the other 3 sides and leave you an easy, breezy outdoor shower experience. An outdoor shower will be up against the elements, and regular water will warp and ruin wood if you don't take precautions. Use an outdoor sealant and finisher to protect your shower for years to come.
Consider how much drainage you'll need when constructing the floor and walls. Tramp down a thick layer of gravel for easy, cost-effective flooring. Build a simple wood floor for a professional looking shower. Use plywood or corrugated metal sheets with wooden posts for a simple, customizable wall. Purchase pre-built outdoor shower walls for a professional, easy finish. Use a curved shower curtain to build an easy wall around your shower. Stain and finish any wood so that it is waterproof.