Nonlinear analyses of RC(Reinforced Concrete) columns considering time dependent behavior of concrete are conducted, and an improved criterion to estimate the design load carrying capacity of slender RC columns is proposed. To simulate the material nonlinearty including the cracking of concrete, the layer model is adopted, and the initial stress matrix is considered for the simulation of P-Δ effect. In advance, the time-dependent deformation is formulated with the first-order algorithm based on the expansion of a degenerate kernel of compliance function. After correlation studies with previous numerical results and experimental data to verify the efficiency of the developed numerical model, many parameter studies are followed, and a regression formula which can give more exact resisting capacity of slender RC columns is introduced on the basis of the obtained numerical results.