Methods and apparatus for stimulating oil or gas wells using material cemented outside the casing. Reaction agents, usually comprising oxygen-rich material and a coil of high order explosive, are positioned around the outside of the well casing at a desired level in a carrier and reacted later. The stimulation operation is initiated by firing a shaped charge into the high order explosive material. The combination of the explosive force of the high order explosive and burning of the oxygen-rich material fractures and cleans the formation adjacent to the well casing. The reaction agents may be provided in a sleeve supported on the casing joint at the time it is inserted into the well. In another embodiment, all components would be cemented externally to the casing and reacted remotely by a coded signal.