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The maximum stress in a storage vessel generally occurs in the region of the support. In the case of twin-saddle-supported horizontal vessels used for liquid storage under modest operational pressure, the strain on the inside surface of the vessel, at the top of the support, is tensile. This can create problems in glass-reinforced plastic (GRP) composite vessels since local cracking of the inner surface may allow liquid ingress to the glass through the matrix with consequent premature local failure. This paper extends the earlier work done at the University of Strathclyde, Glasgow, on metallic vessels (assumed isotropic) and outlines a thin-shell analysis, appropriate for the layered GRP vessel, to derive the strain levels in the support region. Over several years experimental work has been carried out on a range of GRP vessels of various sizes. Of particular note three full-size GRP vessels have been extensively strain gauged and hydraulically tested to provide experimental results to validate the theoretical analysis. Using this analysis, a parametric survey has been conducted and a design approach presented, to enable the maximum strain to be determined for the symmetric laminated horizontal vessel.