The American Society of Mechanical Engineers (ASME) maintains the technical standards for the maximum allowable stress on the walls of a pressure vessel, such as a vacuum tank. The formulas from Section VIII, Division 1 of ASME codes calculate the value using the maximum allowable working pressure inside the tank and incorporate a safety factor of four. To calculate actual vacuum tank stress for a given working pressure, use that pressure in the calculation and multiply the final result by four.
Things You'll Need
 Wall thickness, excluding corrosion allowance, in inches
 Working pressure, in psi
 Inside tank diameter, excluding corrosion allowance, in inches
 Joint efficiency

Divide the working pressure by twice the joint efficiency. For an example, with a working pressure of 90 psi and a joint efficiency of 0.9, the result is 50.

Divide the tank diameter by the wall thickness. For this example, 60 inches divided by 0.6 inches yields 100.

Add 0.2 to the previous result. Continuing with the previous numbers, 100 plus 0.2 is 100.2.

Multiply the results from the previous steps together to get the maximum allowable tank stress, if 100 psi was the maximum working pressure. With the example numbers, the result is 5,010 psi.

Multiply the previous result by four to remove the safety factor and find the actual vacuum tank stress. The result in this case is 20,040 psi.
Tips & Warnings
 This calculation is for ellipsoidal tanks, the most common shape for production facility vessels. The calculations for cylindrical, hemispherical and conical vessels differ slightly.
References
 Photo Credit Propane Tank image by John Walsh from Fotolia.com