This investigation is concerned with the stresses in a hollow circular cylinder of constant wall thickness, and closed by flexible plates, also of constant thickness. The cylinder is subjected to the combined action of an internal pressure and an axial force, both of which are statically applied. Although the particular case envisaged is that of a shock absorber, there are other engineering elements to which the analysis is applicable. Any closed circular cylinder of constant wall thickness subjected to an internal pressure is within the category. In a paper, Dr. D. M. A. Leggett investigated the case of an oleopneumatic shock absorber with rigid end plates, and what follows is an extension of his paper. As would be expected, the flexibility of the end plates causes a reduction in the flexural stress.