Missouri Revised Statutes Title VI. County, Township and Political Subdivision Government § 49.610. Variances may be granted by county commission, when

Any order or ordinance regulations adopted pursuant to sections 49.600 to 49.615 shall provide that the county commission may grant individual variances beyond the limitations prescribed by the order or ordinance regulations upon presentation of adequate proof that compliance with the provisions of the order or ordinance regulations will result in an exceptional hardship to applicant or any arbitrary and unreasonable closing or prevention of any lawful construction, use or other development in the area or county and which will not result in additional threats to public safety and will not be inconsistent with the objectives of sound flood plain management.