This paper presents a new numerical model for the nonlinear inelastic analysis of biaxially loaded high strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns. The numerical model considers the effects of progressive local buckling, initial geometric imperfections, high strength materials and second order. The accurate fiber element method is used to model the inelastic behavior of composite cross-sections. Theoretical models are developed that simulate the load-deflection responses and strength envelopes of thin-walled rectangular CFST slender beamcolumns under biaxial loads. New computational algorithms based on the M ller's method are developed to adjust the depth and orientation of the neutral axis and the curvature at the columns ends to obtain nonlinear solutions. The numerical model developed is shown to be an accurate and efficient computer simulation and design tool for biaxially loaded high strength thin-walled rectangular CFST slender beam-columns with large depth-to-thickness ratios. The verification and applications of the numerical model are described in a companion paper.