Lateral/multilateral drilling technique has significant potential to reduce well costs and increase hydrocarbon production. Coiled tubing drilling (CTD) takes a very substantial role in lateral/multilateral drilling. Well cost reduction in CTD can be achieved by transmitting weight to the bit effectively and preventing coiled tubing (CT) failure/fatigue and lock-up occurrence. To acquire this goal, an accurate buckling model becomes essential. This paper presents a new buckling model in a hole of constant curvature (such as the build section of a horizontal well). It starts from the formulation of the change in the strain energy of bending, the potential of the axial force and the potential of the radial force. Using the energy method, new equations are derived to predict the axial compression force to maintain stable sinusoidal configuration and the axial compression force required to produce helical configuration. Examples show that the axial compression loads to produce sinusoidal and helical forms are much larger than those in deviated wells, especially in short radius wells.