A numerical procedure for the analysis of slender arch buckling problems for uniform dead weight is presented in this paper. Such loading changes in the arch profile. The problem is nonlinear. The numerical procedure is limited to an inextensible analysis and to elastic behavior. Based upon a numerical integration technique developed by Newmark for straight beams, a large deflection bending analysis is combined with small deflection buckling routines to formulate the numerical procedure. The numerical procedure is composed of a combination of the numerical integration and successive approximations procedure. The results obtained in this study are as follows : 1. The critical loads obtained in this study coincide with the results by Austin so that the algorithm developed in this study is verified. 2. The numerical results are converged with good precision when the half arch is divided into 10 segments in both Prime and Quadratic section. 3. The critical loads are decreased as the ratios of rise versus span are increased. 4. The critical loads are increased as the moments of inertia at the ends are increased. 5. The critical loads of Prime section are larger than that of Quadratic section under the same profile conditions.