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It is widely acknowledged that tracking the postbuckling response of structures made from thin plates can be problematical. Such difficulty is associated with highly nonlinear effects including mode jumping, imperfection sensitivity and their combined interactions. Two widely used techniques that are currently used involve path following and asymptotic expansion. The former is often implemented in commercial finite element codes but can prove unreliable at representing branch switching. The latter is a relatively quick technique due to its recursive linear nature but is only reliable in the vicinity of bifurcations. Due to the overall complex nonlinearity, analytical closed form solutions do not exist for path following and rarely for quadratic asymptotic expansions where simple forms have been adopted. This paper presents an analytical-based approach that enables the efficient optimal design of moderately deep nonlinear postbuckling behaviour of laminated composite plates under uniaxial or biaxial loading. It provides a closed form solution that more reliably reflects deeper postbuckling response than the state-of-the-art. Subsequently, highly efficient postbuckling optimization is attributed to the newly derived closed-form solution and a recent two-level optimization framework.