A method and an apparatus are disclosed for processing waste matter which is difficult to dispose of. The waste matter is incinerated by radiation of heat from material which exhibits microwave absorbing properties and is heated upon such absorption. The secondary gaseous waste matter produced by the incineration is burnt or pyrolysed by the presence of microwave absorbing material which is also heated by absorption of microwaves. The process according to the present invention can be practiced in an continuous operation and the volume of waste matter is remarkably reduced by the process and apparatus according to the present invention.