Optimization for the insulation thickness and external shape of a household refrigerator is peformed in order to minimize thermal load through the insulation wall. The one dimensional conduction heat transfer model is adopted to calculate thermal load. Calculus of variation is employed to optimize the thickness and shape of refrigerator or freezer. The uniform distribution of an insulation thickness and cubed external shape make thermal load minimize. Finally, by using both of the computational and experimental method, the thermal load is minimized for a refrigerator/freezer. It is shown that there exists optimal thickness of insulation walls and external shape for given the external cabinet dimensions and freezer and refrigerator internal volumes, Also, the analytical results are well agreed with the experimental results.