Abstract: The theory on the closure deformation of the elliptical crack surface in brittle materials under compressive loadings is studied by the method of complex functions and conformal transformations. Based on the theory, a simplified formula is established to determine the closing stress of an open crack. Comparisons of the closing stress between the simplified formula and previous theory are made, and the result shows that only small error happens by using the simplified formula, which verifies the validity of the simplified formula. Referring to the experiments, the finite element method is used to simulate the closing process of the open crack under compression, and the numerical results support the theoretical viewpoints in the paper: an open crack exists only in the state of being completely closed or completely open under compression. Based on the analysis of the displacement curves of the nodes in the finite element model, a new numerical method is presented to determine the closing stress of an open crack. Finally, the closing stresses solved separately by the numerical method, the previous theoretical formula and the simplified formula are compared, and the result shows that the closing stresses obtained by the three methods are identical, which supports the proposed conclusion in the paper.