Offshore pipelines are increasingly being employed to transport offshore hydrocarbons to onshore processing facilities. Pipelines laid directly on the seabed are subject to a considerable hydrodynamic loading from waves and currents and must be accurately designed for on-bottom stability. Confidence in the stability of pipelines requires appropriate models for their assessment and, in this paper, particular emphasis is placed on achieving an integrated and balanced approach in considering the nonlinearities and uncertainties in the pipe structure, the reaction of the restraining soil, and the hydrodynamic loading applied. A statistical approach is followed by developing a response surface model for the pipeline maximum horizontal displacement within a storm, while including variability in parameters. The Monte Carlo simulation method is used in combination with the developed response surface model to calculate the extreme response statistics. The benefit of this approach is demonstrated and also used to investigate the sensitivity of the on-bottom pipeline simulation for a variety of model input parameters. These results provide guidance to engineers as to what uncertainties are worth reducing, if possible, before a pipe is designed.