A three-dimensional analytical model of the mechanical response of a bonded layered flexible pipeline section to a general set of loads and pressures is presented. Stiffness relations for isotropic, orthotropic and helically wound armoring layers are developed and combined to form a total section stiffness equation incorporating inter-layer pressures and radial deformations. These layers may be used to model the mechanical responses of flexible pipelines including any number and order of layers. Typical loads are taken from a three-dimensional analysis of a flexible production riser in a steep-wave configuration in 310 m water depth. An illustrative pipe section with five layers, including an inner steel tube, two contrawound steel cable layers and two modeled with rubber matrix materials, is subjected to this three-dimensional load set. Computations show the dominant influence of the steel strands in carrying the ambient loads and also gives an accurate picture of the radial distribution of inter-layer pressures across the pipe thickness. The analytical model is designed to give a detailed assessment of deformations and stresses in the various layers such that estimates may be made of critical parameters including wear, slip, rupture, debonding and other related aspects of flexible pipe performance.