S U M M A R Y Rheological parameters describe properties of the lithosphere, but it is generally impossible to measure them in situ. Thus a model has to be developed to relate parameters to observables. We consider flexure of the oceanic lithosphere. A quantitative representation of a brittle-elastic-ductile rheology is based on a semi-empirical model. The non-linear problem of plate flexure is solved by the multiple-shooting algorithm using a Runge-Kutta procedure from analytical solutions for an elastic model. The bending moment and its derivatives have been deduced analytically to improve the accuracy and speed of computations. A family of numerical solutions was built that describes flexure of the oceanic lithosphere at subduction zones for various ages, strain rates, and activation energies. Relative contributions of rheological parameters are discussed. The model is then used to evaluate rheological parameters of the Kuril trench from gravity data. The strain rate estimates are found to be about 3. 10-('6*1)s-1 assuming creep activation energies between 520 kJ/mole and 550 kJ/mole for lithospheric age ranging from 90 Ma to 110 Ma.