Introduction RIFLEX is a computer program for analysis of flexible risers and other slender structures, such as mooring lines, fish cage systems, pipelines and also conventional steel risers. In addition to this Theory Manual the program documentation consists of: User Manual: Description of system modelling, input and output data. This manual gives a description of - and references to - basic theoretical and numerical methods as used in the program. The finite element formulation is described in Finite Element Formulation, including some guidance to system modelling. The static analysis methods comprise catenary analyses, available for a limited range of systems, Static Catenary Analysis, and a fully nonlinear FEM analysis, Static Finite Element Analysis. Guidance to load sequence selection is given in Static Finite Element Analysis. Dynamic analysis comprises linear and nonlinear time domain analysis, Dynamic Time Domain Analysis and Eigenvalue Analysis. Hydrodynamic and aerodynamic load models and forced motion excitation are described in Load Models, and contact force models in Contact Formulation. Methods and options for result processing and data reduction are described in Result Post Processing. Matrix Plot Result Finite Element Formulation