This paper presents a sensitivity analysis on a numerical tidal stream turbine model where a multitude of input parameters’ effect on the load output were determined. The statistical procedure used, known as the Morris method, provided insight into the interactions between the parameters as well as showing their comparative influence on the turbine loading. The investigation covered parameters from the operational, geometric design and inflow variable domains where the rotor radius, current shear, blade root pitch, surface velocity and wave height were identified as most influential. The blade pitch was regarded as a surprisingly prominent influence on the loads. The turbine’s operating depth and the blade geometry were also found to be of limited influence in the ranges investigated. In terms of load transmission into the internal components of a turbine’s drive train, the rotor out-of-plane bending moment, or eccentric bending moment, was found to be a considerable contribution to the off-axis loads on the shaft. Therefore, special attention was paid to the input parameters’ relationship to the eccentric load component by performing a detailed study on the load variations caused by the identified primary input parameters. It is concluded that performing a sensitivity analysis on a tidal stream turbine in a specific operating climate can yield insight to the expected load range and that the eccentric loading transmitted to the shaft is significant for most input cases.