High temperature combustion apparatus incorporating a pneumatically suspended combustion zone and capable of supporting relatively high combustion temperatures, in excess of 2400.degree. C. (4352.degree. F.) for essentially total combustion with minimal pollutant production. The combustion apparatus may be employed for waste material incineration in general, toxic waste incineration, and for smokeless burning of wood and vegetation. The combustion apparatus may be employed in an efficient steam electric power generating plant which employs municipal solid waste as fuel, and/or in combination with a magnetohydrodynamic (MHD) electric generator. The pneumatically suspended combustion zone is created by having streams of combustion air directed upwardly from a floor grate and from the sides of a combustion chamber such that combustion occurs in a swirling turbulent mass which does not directly contact either the walls or the floor of the combustion chamber. The relatively high combustion temperatures are sustained by providing a high volume of excess combustion air, the same combustion air which maintains the pneumatically suspended combustion zone. High combustion temperatures are contained with little use of refractory materials, and without melting the combustion chamber sidewalls.