When storing liquids at high temperature in horizontal vessels, the current design methods aim to minimise the thermal stresses by introducing a sliding surface at the base of one of the twin saddle supports. However, regular site maintenance is required to ensure that adequate sliding is achieved. This may be difficult and costly to carry out. The aim of the present work, therefore, is to dispense with the sliding support and to provide saddle designs which, although fixed to the platform or foundation, do not result in the storage/pressure vessel being overstressed when thermal loading occurs. This paper provides general recommendations for the most appropriate saddle geometries, and details the way in which design-by-analysis and fatigue-life- assessments may be carried out using the stresses that arise from these designs.