Investigation of the behavior of embedded box-type reinforced concrete (RC) structures for nuclear power stations subjected to lateral earthquake earth pressure, concerning shear rigidity and its reduction, has been conducted analytically in this study. A nonlinear finite element approach based on smeared crack model of RC plate element was utilized. From the parametric study of a real RC duct for accommodating emergency cooling water pipes in nuclear power stations, it was found that lower reduced shear rigidity factor, which was defined as the ratio of reduced and initial shear rigidity, could be attained by arranging lower concrete compressive strength, higher yield strength of reinforcing bar, higher reinforcement ratio and thinner wall thickness of the RC duct. Finally, a formula to predict the reduced shear rigidity factor has been proposed based on the parametric study.