Cylindrical shells, with a wall thickness-to-diameter ratio of around 1:5000 are found in large steel tanks in the petrochemical industry. In these tanks, the bottom is welded on to an annular plate, under a condition of restraint that corresponds closely to a built-in end. The condition at the top differs depending on the type of design. The extreme flexibility of these tanks has made them liable to buckling under radial pressure. A simplified method of analysis, capable of predicting the buckling pressure of cylindrical shells with varying degrees of end restraint is presented and compared to published results. The case of the free end is given special attention since no complete analytical solution is known to the authors.