A new ultra-rapid process of flash spark plasma sintering is developed. The idea of flash spark plasma sintering (or flash hot pressing - FHP) stems from the conducted theoretical analysis of the role of thermal runaway phenomena for material processing by flash sintering. The major purpose of the present study is to theoretically analyze the thermal runaway nature of flash sintering and to experimentally address the challenge of uncontrollable thermal conditions by the stabilization of the flash sintering process through the application of the external pressure. The effectiveness of the developed FHP technique is demonstrated by the few seconds-long consolidation of SiC powder in an industrial spark plasma sintering device. Specially designed sacrificial dies heat the pre-compacted SiC powder specimens to a critical temperature before applying any voltage to the powder volume and allowing the electrode-punches of the SPS device setup to contact the specimens and pass electric current through them under elevated temperatures. The experimental results demonstrate that flash sintering phenomena can be realized using conventional SPS devices. The usage of hybrid heating SPS devices is pointed out as the mainstream direction for the future studies and utilization of the new flash hot pressing (ultra-rapid spark plasma sintering) technique.