In a hydrocarbon drilling operations, when an axial load is applied beyond a critical value the coiled tubing (CT) will buckle forming sinusoidal wave and with increasing the axial load the CT ultimately goes into a helical configuration. The higher number of contacts between the CT and the wellbore the more friction is introduced. Increasing the CT friction, due to increasing the area of contact with the wellbore, eventually leads to lock-up length beyond which the drilling cannot proceed further. Vibration is understood to be a well-known technique to reduce friction between contacting bodies in many engineering systems. An in-house experimental setup is developed to imitate the wellbore being drilled with the presence of vibrating facility that has the capability to vibrate the CT axially. The setup is employed to examine the effects of amplitude and frequency of vibration on the friction force, between the CT and the wellbore, and on the axial load transfer or the weight on bit (WOB) of the CT. Response surface methodology is used to produce a prediction model to determine the effects of various amplitudes and frequencies the WOB of the CT. The investigations have shown that both amplitude and frequency of vibration have positive effects on reducing friction force and increasing WOB. The actual and predicted optimal designs are also presented in this work.