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The failure criteria and the constitutive relation of materials for an early-age concrete are the most common reasons to conduct the nonlinear analysis and to assess the concrete structures during the construction stage. The delay of theoretical advancement in this field resulted into a mismatch between the rough theories and the advanced algorithms, which were adopted for the estimation and analysis of early-age concrete structures. It is often impossible to find an appropriate way to determine the failure criteria and its constitutive relation that may serve as a baseline. As a consequence, the development and the application of advanced techniques of construction, for example, early dismantling construction technique of formwork, have severely been restrained. Therefore, the study of the failure criteria and its constitutive relation of concrete materials at early-age are important. In this paper, the cubic compressive strength, the prismatic compressive strength, and the axial tensile strength are determined by carrying out a strength test on C20 concrete material at an early-age. Next, the failure criteria of C20 early-age concrete material in the octahedral stress space have been studied and analyzed by using the regression analysis and by deriving the mathematical relation.