Optimization of the transmission case, referred to as gearbox case, has received significant interest in research and practical community for decades. The gearbox case is a key component of rice transplanters since it tends to break while working if irrelevantly designed. In realistic work conditions, rupture and vibration issues commonly exist in the gearbox case of rice transplanter. Therefore, it is necessary to improve the defects of the gearbox case with optimized design. In general, stress, stiffness and norm modes have effects on rupture and vibration issues. Therefore, the optimization of gearbox case should be taken into account both the static and dynamic performance. At the same time, size and shape optimizations are simultaneously incorporated, while both the size and the shape design variables are considered. Associated linear static load cases including the stress and displacement analysis and linear dynamic load case including modal frequency response analysis are utilized to furnish optimization responses. The performance and relevant constraints include the first order natural frequency in normal mode analysis, the deflection under unit load in global axial directions, the velocity versus frequency curve from modal frequency response analysis. The corresponding threshold values are assumed for all constraints accordingly. Eventually the optimized design of gearbox case proposes a highly effective material minimization scheme, which not only dramatically reduces the weight of gearbox case without compromising the integrity of structure but also meets all the performance requirements considered at the beginning of optimization process. Furthermore, non-linear explicit analysis, which is more reliable than regular linear analysis, was employed and justified with remarkable enhancement in structural stiffness from a more realistic perspective. By utilizing the ARSM (Adaptive Response Surface Method) as the optimization engine, the mass of gearbox case has been deducted by 5% on the premise of satisfying all constraint conditions. The local stiffness and the 1st-order natural frequency are improved accordingly. Therefore, rupture and vibration problems are solved. Taking advantage of the methodology proposed in this study, the optimizations of gearbox case can be easily tuned when actual testing data and industrial criteria are available. In addition, multi-objective optimization focusing simultaneously on a number of various performances can also be adopted by using HyperStudy when necessary.