In this paper, the main objectives are to investigate and select the most suitable parameters used in particle swarm optimization (PSO), namely the number of rules (nrule), population size (npop), initial weight (wini), personal learning coefficient (c1), global learning coefficient (c2), and velocity limits (fv), in order to improve the performance of the adaptive neuro-fuzzy inference system in determining the buckling capacity of circular opening steel beams. This is an important mechanical property in terms of the safety of structures under subjected loads. An available database of 3645 data samples was used for generation of training (70%) and testing (30%) datasets. Monte Carlo simulations, which are natural variability generators, were used in the training phase of the algorithm. Various statistical measurements, such as root mean square error (RMSE), mean absolute error (MAE), Willmott’s index of agreement (IA), and Pearson’s coefficient of correlation (R), were used to evaluate the performance of the models. The results of the study show that the performance of ANFIS optimized by PSO (ANFIS-PSO) is suitable for determining the buckling capacity of circular opening steel beams, but is very sensitive under different PSO investigation and selection parameters. The findings of this study show that nrule = 10, npop = 50, wini = 0.1 to 0.4, c1 = [1, 1.4], c2 = [1.8, 2], fv = 0.1, which are the most suitable selection values to ensure the best performance for ANFIS-PSO. In short, this study might help in selection of suitable PSO parameters for optimization of the ANFIS model.