This study discusses the development of a finite element analysis (FEA) model that describes the bending and straightening process of coiled tubing (CT) at the wellhead and the buckling process after CT is run in wells. On this basis, this study calculates the initial residual bending configuration quantitatively for the first time and describes the residual stress and strain-changing regularity. The initial residual bending configuration of CT under wellbore constraints after running into the hole is sinusoidal, which essentially affects the CT downhole mechanical behavior. Simulating the buckling process of the CT string in the vertical and horizontal sections with the CT string assumed straight served as control subjects. This study verifies the accuracy of the numerical simulation method by comparing the results of critical buckling loads to previous research results. The initial residual bending configuration significantly affects axial load transfer and reduces the least axial force required to produce a helical buckling in the wellbore. The residual stress induced by the bending and straightening process at the wellhead makes the buckling and buckling release of CT downhole an elastic-plastic process, whereas it becomes an elastic buckling process if the initial configuration of the CT string is assumed straight. The comparison between the buckling process of CT with residual bending and CT without residual bending shows that the effect of residual bending on CT cannot be ignored when studying the downhole mechanical behavior or job design.