The growth in the use of high pressure by the chemical industry in the 20th Century led to the discovery of polyethylene by ICI in the 1930s. At that time, the pressures required by the large‐scale production of low density polyethylene were well beyond normal design practices for continuously operating plants and the development of the process in both the United States and Europe posed formidable problems. This led to a number of different modifications to the high pressure procedures used by ICI. In this article, the basic principles governing the design of thick‐walled cylinders to withstand static high internal pressures are reviewed. It is shown how these principles together with much of the work carried out since the 1940s, especially that directed towards increasing fatigue strength of cylinders subjected to pulsating internal pressure were used to develop both stirred and tubular reactors and pumps. Compressors play a vital part in these processes and are discussed in detail. Most of this article is devoted to the design of continuous chemical plants