Subsea pipelines and cables are important infrastructure in the offshore environment, particularly for conveying hydrocarbon and electricity. Failure of such lines can lead to significant environmental and economic impact, and potentially loss of life. Prediction and mitigation of the risk of failure is therefore extremely important. One of the major threats affecting the structural integrity of subsea pipelines and cables is vortex-induced vibration (VIV) which causes repeated occurrence of high values of stress which, when accumulated, can lead to fatigue failure. Existing design practice applies relatively high safety factors and is limited in application, particularly with regard to the influence of bed proximity on dynamic response and hence fatigue design. This study aims to reduce conservatism in design practice by the development of a computationally efficient numerical method to analyse the effect of wall gap ratio (e/D) on dynamic response of free spanning pipeline. A reduced order method (ROM) has been developed for this purpose in which pipeline response is simulated using an FEA model with sectional forcing obtained from multiple CFD simulations of a 2D freely supported cylinder near a wall for a range of mass-damping ratios. This approach is validated relative to experimental measurement of response of a free span in unconstrained flow with the magnitude of peak deformation to within 5% and fatigue damage over a range of reduced velocity in the range 5-12%. This is shown to be more accurate than a widely used wake oscillator which is also computationally less costly than full two-way Fluid-Structure Interaction simulation. The validated ROM, when applied to a cylinder pinned at both ends, it predicts a lower fatigue load, by a factor of two to three than the widely used DNVGL-RP-F105 in the industry, thus offering scope for significantly reduced design conservatism. Applied to a flexible cylinder close to a wall (e/D < 2) the method leads to fatigue load predictions that are between 12.5% to 25% of those obtained by the standard design method.