Liquefied natural gas(LNG) cargo containment system(CCS) has the primary function of ensuring both adequate structural safety with respect to sloshing load which is defined as a violent behaviour of the liquid contents in CCS due to external forced motions and thermal insulation keeping natural gas below its boiling point. Among different LNG CCS types such as independent B-type and membrane ones, Mark III CCS is considered in this paper to perform its strength assessment. Mark III CCS plate is designed and constructed by stacking various non-metallic engineering materials such as plywood, triplex, reinforced PU foam that are supported by series of mastic upon inner steel hull structure. From the viewpoint of structural analysis, this plated structure is treated as a laminated composite structure showing complex structural behaviour under external load. Advanced finite element models of Mark III CCS plate is generated and used in conjunction with ultimate strength based failure criteria from laminated composite mechanics for the strength assessment. The strength assessment is performed within the initial failure state of Mark III CCS plate. Results provide failure details such as failure locations and loads. Finally obtained results are reviewed using the loads from acceptance criteria suggested by classification.