In this paper, the assessment of peak factors for aerodynamic loading on an anticlastic conical tensile membrane structure (TMS) is carried out along with a comparative study of several prediction models. The Unsteady Reynolds-Averaged-Navier–Stokes (URANS) based CFD simulations of a turbulent boundary layer around the TMS are used to obtain the time-varying aerodynamic loading (in the form of wind pressure coefficients) and associated peak factors on several representative locations on the TMS surface. The statistical moments of skewness and excess kurtosis are employed to categorize these locations into Gaussian and non-Gaussian regions. It is observed that points near the corners and the edges from where the flow separates have prominent non-gaussian behaviour with higher peak factors. The observed peak factors are compared with those from several prediction models namely the Davenport, Modified Hermite, Translated Peak Process (TPP), and Liu’s models. Root Mean Squared (RMS) errors are calculated for each case to quantify the extent of difference between the observed and predicted peak factors and it is conclusive that the Modified Hermite model predicts the best whereas, the Davenport model has the poorest prediction capability.