Two vessels with torespherical heads were pressurized to destruction. The objective was to determine pressures at which observable or measurable indications of failure could be detected. For Vessel 1@ the only observable action was a slow formation of some waviness of the knuckle profile. It lost pressure at 700 psi when a crack developed at a nozzle weld at the bottom of the shell. For Vessel 2@ no indication of any sign of failure was observed until it burst at a pressure of 1080 psi by ductile fracture along the longitudinal weld of the shell. After-test examination revealed no measurable waviness of the knuckle. The main conclusion is that there is a problem in the applicatioan of the double elastic slope collapse criterion to torispherical heads. It was determined that when using this criterion a collapse pressure signaling excessive deformation cannot be determined with any certainty. For a material with sufficient ductility@ the use of an estunated vyrst oressyre aooears oreferavke@ A design criterion based on the membrane stress at the crown of a torispherical head reaching the ultimate tensile strength is proposed. Publication of this document - WRC Bulletin No. 414 was sponsored by The Pressure Vessel Research Council of the Welding Research Council@ Inc.