Considerable eftects of geometric nonlinearity upon tallsteel frames and flexibly jointed steel frames are recognized.Systematicanalysis philosophy of geometric nonlinearity under various coordinatesystems and its corresponding explicit expression of tangent stiffness matrices are comprehensively embodied.The entries in tangent stiffnessmatrices with its nonlinear behavior and its abstrusely implied physicmeanings are expounded and a straight forward derivation technique ofnonlinear matrices is given.A computer algorithm which can performwhole range studies of steel frames by considering geometric and materialnonlinearities up to the ultimate load carrying capacity is implemented.