The burning regulations for Missouri are controlled by the Missouri Department of Natural Resources.  Click here for the link to their page.  The basic regulations on open burning is that it is allowed between September 16 to April 14 every year.  Fires must not exceed 4 foot by 4 foot in size.  Fires must not be started until 10:00am and must be extinguished by 4:00pm.  They must be attended at all times.  They also may only contain natural vegetation.  Wind speeds should be below 15mph.  Any violation of MoDNR regulations can bring a fine up to $20,000.