Composite material driveshafts can be the optimal choice for various high performance and heavy-duty power transmission applications, due to their light weight and high strength. Especially for the marine sector, composite driveshafts also offer the advantages of high fatigue and corrosion resistance. Composite shafts can be 25–80% lighter than the conventional steel shafts of similar specifications. Recent experimental and analytical studies on composite driveshafts conducted in the Shipbuilding Technology Laboratory of NTUA have revealed some significant discrepancies between their expected and eventual mechanical response. There are several factors that could contribute to these discrepancies that are related to the uncertainties in the manufacturing of composite materials. The mechanical properties of the composite, the winding angle, the thickness and the length of the driveshafts are distinguished as the more important factors affecting their mechanical response. This study aims to quantify the uncertainty induced by the deviations of the mechanical and geometrical properties of the driveshafts on their mechanical response and to determine its expected range. The possible ranges and distributions of the critical parameters are investigated and are then propagated to the estimation of the mechanical response of composite driveshafts, in terms of torsional stiffness and buckling load. Monte Carlo statistical simulations are employed to solve the problem at hand. The resulting probability density functions help to identify the probability of the occurrence of the experimental measurements and determine the likely causes of the discrepancies. The study aims to support the design and production of higher quality composite driveshafts for marine applications.