A solving method with complex variable function which is fit for numerical calculation for stress concentration phenomena on an infinite plate where there are curvilinear holes is described in this paper. According to the method, the computer programs are made to study the stress concentration problems with curvilinear holes (hexagonal form and oblate form) that are often used in ship and other engineering structures. The maximum of the stresses at the edge of the holes and the distribution of the stresses under axial loading and pure bending moment are calculated respectively. Furthermore, the variations of factors of stress concentration with the different proportions of length and width for oblate holes are considered. The influence on factors of stress concentration due to the change of plate width is indicated. The solutions are consistent with the numerical results of boundary element method, finite element method and related articles.