I read in one paper that collagen fibers in dermis are randomly oriented in direction with respect to the skin surface. I can't locate that paper now. However, I came across this paper that indicates that collagen is always aligned parallel to the skin surface (page 3). Which one is correct?
Collagen underneath the epidermis is not completely randomly oriented, in fact mostly they are directed along the muscle fibres beneath them.
This was first observed by Karl Langer and hence was given the name as langer's lines( of skin tension). This peculiar arrangement of collagen is responsible for maintaining integrity of skin at times of stretching force developed on them by the muscles. Had they perpendicular, then skin would tear easily.
This also has clinical relevance because during surgery if an incision is made along these lines the scar would be minimum.