This paper deals with the behavior of high-pressure unbonded flexible steel pipes which can be used as risers in offshore applications. It concerns primarily the behavior of the internal structure of the pipe. A theoretical approach allows to establish simple formulas for evaluating: the stresses, and the contact pressures between layers due to axisymmetrical loads; the stresses due to bending; the relative slip between layers due to bending. This is a first step towards the evaluation of the life expectancy of flexible pipes. It must be completed by the determination of friction and wear factors through test results.