There are several reasons for a hard lump under the sebaceous process. The first is a sebaceous cyst, which is a localized cyst caused by a sebaceous gland that is secreting normally, but is blocked in the skin or in an internal duct. It is relatively tough and usually has no local pressure pain, but can be painful if accompanied by infection. The second common cause is localized infection. This condition is usually accompanied by redness and swelling of the skin or surrounding tissues, and pressure pain is more pronounced. The third common cause is lipoma. Most lipomas are soft, but there are special cases where they are hard or tough.