For a shall-issue gun law, authorities (usually the local police) are required to issue a concealed carry permit to any individual who request it if he meets the state's issuance criteria, often a background check and a safety class.
The following are undisputed shall-issue states: Alaska, Arizona, Arkansas, Colorado, Florida, Georgia, Idaho, Indiana, Kentucky, Louisiana, Maine, Michigan, Minnesota, Mississippi, Missouri, Montana, Nevada, New Hampshire, New Mexico, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, Washington, West Virginia, and Wyoming.
Alaska is both a "shall-issue" and an "unrestricted" state. Alaska does not require a permit for any law-abiding individual to carry a handgun, either openly or concealed, within the state's borders. However, the state continues to issue permits to any of its residents who meet the state's issuance criteria.