Coiled tubing is utilized in a variety of oil well operations. For applications such as drilling, completions, and remediation, coiled tubing offers the benefits of reduced costs, increased insertion speed, and reduced environmental impact. Coiled tubing possesses a limitation, however, in that it can buckle in service causing damage to the tube and disruption of operations. There have been numerous papers published during the last 50 years on helical buckling. Numerous fast running engineering codes have been developed to determine the onset of sinusoidal buckling, helical buckling, and lock-up of drill pipe in a wellbore, with particular emphasis on coiled tubing. We provide a methodology for evaluating the complete nonlinear mechanical behavior of coiled tubing insertion from a first-principles finite element modeling perspective. Using this approach the buckling, post-buckling, and lock-up behavior of the drill pipe can be studied. Additionally, post lock-up methods such as vibration loading and downhole lubrication can also be evaluated.