Try this and see if that solves your issue.
You may be using the right technique of stretching the elastic as you sew, but you may have the wrong kind of elastic. All elastics are definitely not equal. Or, you may be using too short a stitch or stretching the elastic too much or not have the right kind of elastic for the fabric you are using, etc.
I find I have better results if I use a stretch needle and a longer stitch length (between 3 and 4) when I sew elastic.
I like Stretch Elastic and Ban-Rol as well as Stretch Sew-elastics. You can find them online. I usually cut them about 4 inches smaller than my actual waist when I am sewing an elastic waistband. This is a matter of preference. You may like the elastic 5-7 inches smaller or even greater. Stretch a length of elastic around your hips. If you can get it over your hips when it is stretched out, you probably have enough. Make a note of what you use so you will know how much you need for future garments.
Don't overlap the elastic. This creates a bulky "bump". Instead, butt the cut ends to make a circle. Then, either wrap this area or place a small piece of fabric or tape under the cut edges. Set the sewing machine for a wide 3-step zigzag and stitch back and forth a few times to secure the elastic together. Test it to make sure it holds before applying it to the garment.
For a waistband, place the elastic just below the top inside edge of the garment and pin at each of the garment and elastic quarter points. These may not fall at the side seams. That's OK. Just divide the fabric evenly.
Now, with the elastic up at the machine, vertically stitch the elastic in place at these points before you begin stretching and sewing. This keeps the elastic from pulling diagonally and you don't have to worry about pins popping out.
Set your machine for a wide long zigzag. You may prefer the 3-step zigzag stitch. Remember that a longer stitch lets the elastic bounce back better. Try a 3 or 4 length.
Continue with the elastic up and stretch and sew around the bottom of the elastic attaching it to the garment. When you fold the elastic down to the inside, this stitching is on the top inside edge.
To complete the elastic, stitch the lower inside edge to the garment. However, if you don't want to see this stitching, some people prefer to just vertically straight stitch the four quarter points (centers and sides) in the ditch to hold the elastic down. It's your choice.
All I ask is please use the Star Rating Link at the top of your page before leaving, that is the only way I am paid anything through the site and that will also get you a DIRECT LINK emailed to you to get back to me!.....tips are greatly appreciated so thank you very much for using this service. If you have any other questions just post back to me here anytime!