The fastening system includes first and second fastening members, each having a backing and rows of rail segments protruding from the backing. The rails segments have a base portion attached to the backing and a cap portion distal from the backing. The cap portion has a cap width that is greater than a width of the base portion. There are rows of posts protruding from the backing of at least the first fastening member. When the first and second fastening members undergo fastening, the posts bend away from the rail segments while the cap portions of the rail segments of the first and second fastening members pass by each other and then return to their original positions after the first and second fastening members are fastened. The fastening system attached to a portion of a package is also disclosed.