A wide-band steady-state model of a tensile-strained bulk InGaAsP semiconductor optical amplifier is described. An efficient numerical algorithm of the steady-state model and a parameter extraction algorithm based on the Levenberg-Marquardt method are described. The parameter extraction technique is used to determine the material Auger recombination coefficient, effective intraband lifetime, the average strain and molar fraction of Arsenic in the active region. Simulations and comparisons with experiment are given which demonstrate the accuracy and versatility of the model.