Originally Posted by andrei_r

You're doing something wrong. Take the deflated new tube, and give it just one or two pump strokes so that it becomes round but doesn't stretch any. Insert the tube into the tire. Mount the tire together with the tube over the rim one bead at a time. Start at the valve. Be careful not to pinch the tube and to make sure the valve is straight. There must be plenty YouTube videos showing how to mount a bicycle tire.