The present paper describes a numerical investigation of the mechanical response of externally-pressurized dented stainless-steel pipes, subjected to reverse cyclic axial loading. This is the first part of a large-scale project, between The University of Edinburgh and Tianjin University, and is motivated by the mechanical response of offshore pipelines, which are often subjected to cyclic loading during installation or operation. Under those cyclic loading conditions, the pipe may collapse because of accumulation of plastic deformations at the dent area. The paper describes a numerical simulation of the above physical problem, in an attempt to support experiments on 50mm-diameter stainless steel pipes, which are being performed at the laboratory facilities of Tianjin University. Pipe segments are subjected to reverse cyclic axial loading (tension and compression), in the presence of external pressure. Prior to the application of external pressure and axial load, the pipes are locally dented, in the form of “smooth dent” or “local ovalization”, so that collapse initiates at the dent area. The numerical simulation is aimed at examining some aspects of pipeline behavior to support and complement the experimental observations. The simulation is conducted using rigorous finite element tools, which account for large displacement and nonlinear material. Towards this purpose, an advanced material model is employed, capable of describing the phenomenological aspects of material response under cyclic loading, such as the accumulation of plastic strain and ratcheting. In the first part of the analysis, the local ovalization (denting) process is simulated. Subsequently, the pipes are subjected to uniform constant external pressure and, keeping the pressure level constant, monotonic or cyclic axial loading is applied until collapse. The numerical results are aimed at identifying the interrelation between the magnitude of the applied loading and the number of loading cycles to failure. The results are presented in diagrams of axial displacement, ovalization and local strain versus the corresponding number of cycles to failure, for specific levels of external pressure.