This paper proposes an optimization technique for increasing the structural integrity of a light-weight composite blast containment vessel. The vessel is cylindrical with two hemispherical ends. It has a steel liner that is internally reinforced with throttles and gusset plates and wrapped with a basalt-plastic composite. A finite element model of the blast containment vessel was proposed and verified in an earlier work. The parameters of the vessel are incorporated within an iterative optimization procedure to decrease the peak strains within the vessel, which are caused by internal blast loading due to an explosive charge placed at the center of the vessel. The procedure is validated for different initial guesses of the design variables.