In reality, downhole conditions are highly unpredictable due to many uncertain and inconsistent factors, such as the uncertainty of the friction and contact between drillstring and bore-hole. As friction and contact are crucial components in torque and drag calculation, it is meaningful and practical to consider their uncertainty. This paper presents a random method for calculation of hoisting drag. Firstly, the finite element method (FEM) is used for hoisting drag calculation of a directional drilling well using Adanoy’s method in the deterministic case. Then two strategies are taken to model the random component in the downhole. The first strategy considers the randomness of the downhole friction. Instead of being a deterministic value, the friction coefficient is considered as Gaussian. The second strategy considers the randomness of contact between drillstring and wellbore. As a result, the drillstring is no longer continuously contacting with the wellbore in the curved section of well profile, which can help avoid overestimating torque and drag. Parametric studies on both strategies are conducted. Monte Carlo (MC) simulation is employed for statistical analysis. The probability density distributions and mean values of drag will be studied. The methodology can be extended into torque or drag calculation in lowering, ream in and ream out drilling conditions. Results from this paper indicate that surface hoisting drag is nearly Gaussian when the friction coefficient is Gaussian. The contact loss leads to considerable reduction in the surface hoisting drag when contact uncertainty is considered. The work of this paper will help estimate the range of surface drag and torque, which allows the well planner to develop a risk assessment for a challenging well trajectory.