Make a trench outlining the perimeter of your flower box that is at least six inches deep and six inches wide. The trench is part of the foundation for your brick flower box.
Mix the concrete with water in a bucket, per the manufacturer's instructions, and pour it into your trench. Make sure the concrete does not overflow. Let the concrete dry and harden for at least 24 hours.
Mix the mortar and water in a bucket, per the manufacturer's instructions, and spread it over the concrete where you want to lay down the bricks. There should be an inch layer of mortar between the concrete and bricks.
Lay the bricks a quarter- to half-inch apart to form the brick flower box. Use a level to make sure the bricks are even. Then, add mortar in between the bricks and to the backsides of the bricks. Built 2 Build suggests you use a "medium layer" of mortar between each level of bricks. Blue Circle Southern Cement says to leave every third vertical joint in the first layer of bricks open to allow for drainage. The vertical joint is the space or gap between two bricks as they lay side-by-side.
Continue to add bricks until you have reached your desire height.
Place plastic lining in the flower box. Cut a piece of plastic lining that is two times higher than the inside of the flower box. Fold it in half and place it around the inside of the brick flower box. Built 2 Build says you can use rocks to hold it in place. The plastic lining should not be so high, however, that it will show above the dirt.