The results of external air pressure buckling tests of thin-walled, truncated conical steel shells are presented, along with a description of the equipment developed for the testing program. The testing was conducted in support of Sandia National Laboratories Z-Pinch Inertial Fusion Energy Proof-of-Principle power plant design. Optimized stiffening ring locations were determined by using the finite element method, and were then tested, indicating an experimental improvement in initial buckling pressure of more than 300% over the unstiffened cone. An analytical method of determining buckling pressures of stiffened conical shells is also presented, based on the method of the equivalent cylindrical shell. The results of the analytical method agreed very closely to the finite element method for the stiffened cones, but are 20-40% higher than the experimental results.