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A fitted bed sheet isn't very useful once the elastic has worn out. If the sheet is still in good condition and you want to keep using it, you have the option of replacing the worn elastic with new. At the very minimal cost of the elastic and thread, you can save yourself the frustration of having to reattach the corners of the fitted sheet every time you make the bed.
Mark the sheet to show where the ends of the elastic are attached. These two marks will represent the attaching points for the new elastic.
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Remove the old elastic from the sheet with a seam ripper. Seam rippers have a narrow and pointed cutting edge that when inserted between stitches will cut the threads.
Measure the width of the elastic and purchase new elastic of the same width. Measure the length of fabric that the elastic was attached to. Subtract 4 inches from the length and cut new elastic according to that measurement. The elastic will be shorter because it will stretch over the corner of the mattress and provide a snug fit to secure the sheet.
Pin the ends of the elastic at the attaching points on the sheet. The elastic is shorter than the distance between the points and will be stretched to fit while attaching the elastic. Flatten the sheet and place straight pins every 2 or 3 inches to secure the elastic and evenly disperse the elastic.
Place the sewing machine foot on top of one end of the elastic. Keep the sheet flat and the elastic stretched while you sew a straight stitch to secure the elastic, this method is called direct application. Continue sewing until you reach the end of the elastic. Secure the stitches at both ends of the elastic by reversing the stitching and moving forward again.
Remove the straight pins as you sew past them and the elastic is secure.
Direct application means to machine stitch the entire length of the elastic to the fabric. Slightly wider elastic can also be used. The zigzag stitch is another option for sewing the elastic to the sheet. Use a ball-point needle to sew the elastic. This type of needle will move freely through the elastic.