A static analysis procedure is formulated and implemented for the numerical determination of nonlinear static equilibrium configurations of deep ocean risers or mining pipes. This implementation involves selection of a finite element model, modeling of structure, surface and subsurface environment and external forces, and solution of nonlinear equilibrium equations. The riser is modeled by three-dimensional beam finite elements which include axial, bending, and torsional deformations. These deformations are coupled through geometrically nonlinear effects. The resulting tangent-stiffness matrix includes three contributions identified as linear, geometric (initial-stress) and initial-displacment stiffness matrices. For the solution, a combination of load-parameter incrementation, state updating of fluid properties, and corrective Newton-Raphson iteration is used. The resulting riser configuration reflects the realistic modeling of environments and external forces. The static equilibrium solution can be used as initial condition for vibration or transient analysis. Numerical studies are presented in Part II of this paper.