The ultimate limit state of buckling is an important consideration for the design of wind turbine support towers (WTSTs) which is increasingly being done with the aid of advanced nonlinear finite element analysis according to EN 1993-1-6. As these towers are relatively slender thin-walled metal shell structures, their response and buckling resistance is invariably affected by geometric imperfections. This paper presents a sensitivity study into the possible relative influences of four different types of realistic imperfections that are likely to arise in WTST construction on the elastic-plastic buckling resistance as assessed by computational GMNIAs. These include idealised but realistic representations of axisymmetric circumferential weld depressions, unintended eccentricities at curved plate boundaries, a global out-of-roundness and corrected parallel flange interface gaps. The relative sensitivity is explored via a ‘one-at-a-time’ (OAAT) study where all factors but one are kept at a constant intensity while the active factor is scaled, with the influence on the computed GMNIA under two load cases recorded. The OAAT study suggests that for shell structures representative of the geometric ranges typical for WTSTs, the weld depression has the most deleterious effect on the predicted buckling resistance.