This paper describes the methods to propose the optimal material properties and construction steps that prevent cracks due to the thermal stresses induced by the hydration heat under the construction of the concrete underpass structures. To achieve the goal of this study, the heat transfer theories were employed and the three-dimensional finite element model of the underpass structure was developed and used for the structural analyses. If the volume of the concrete member that is placed at one time is significantly large, the member is assumed to be the mass concrete and is easy to induce cracks. In order to minimize the cracks during the construction, two different methods can be utilized: one is to arrange the construction steps optimally and the other is to change the materials to reduce the probability of the crack occurrence. In this study, the analyses were performed by considering the changes in material properties with time, the characteristics of the hydration heat generation for cements and admixtures, the volume of the concrete placement at one time, and the environmental conditions.