Steel monopiles are support structures mostly applied for offshore wind turbines. Their installation is straightforward, in particular, in shallow and medium waters. While the wind turbine tower is primarily affected by wind, the wave loads are dominant for the monopile, as it is submerged to a large extent. This study deals with the influence of uncertainties in material and load parameters on the behaviour of those structures. It is investigated how the scattering of material properties (namely Young's modulus of elasticity) affect the structural response. In addition, loads with different characteristics are applied, and it is examined how the changes in loads influence the structural response. The analysed output data of interest are the extreme stresses leading to the accumulation of fatigue damage. In order for a realistic modelling, wave loads are considered with irregular sea states with different wave characteristics (significant wave heights and wave peak periods). The final aim of the analysis is to classify the effects of specific wave characteristics on the stresses by means of a sensitivity analysis. The analysis shows that variations in the wave peak period have the strongest influence on stress outputs. This effect results from the strong sensitivity of the structural dynamical response to the decrease of the difference between the values of the wave peak frequency and the natural frequencies of the structure. © 2017 The Authors. Published by Elsevier Ltd.