The objective of this work is to study the elastic stress distribution, deformation characteristic, and stress concentration factor (SCF) of a cylindrical vessel with lateral nozzle. Three full scale vessels under internal pressure with different geometric dimensions and lateral angle θ(θ=30 deg,45 deg,60 deg) are investigated by both experimental and three-dimensional finite element methods under internal pressure. A detailed stress distribution and the SCFs of the model vessels are provided. The results indicate that the maximum stress of cylindrical vessels with a lateral nozzle occurs at the acute side of the cylinder-lateral intersection and drifts off the longitudinal section of the cylinder for about 20 deg. When the geometric parameters of the vessels (d/D,D/T,t/T) are fixed, the SCF of the structure will increase with a decrease in the lateral angle θ.