Trusses are very often constructed from monosymmetric and built-up cross-sections, which under compression stresses may buckle in torsional or flexural-torsional modes. In fire, this phenomenon is utterly important as failure in trusses may cause the collapse of buildings and result in loss of lives or severe economic impacts. A previous study by Possidente et al. has demonstrated that the buckling curve of Eurocode 3 Part 1-2 (EN 1993-1-2) provides unconservative results for slenderness ranges of practical interest and improved design equations were proposed to increase the safety of compressed members made of angles, tee or cruciform sections at elevated temperatures. As a further step, machine learning (ML) models are developed in this study providing a more accurate yet fast calculation model for compressed members belonging to truss systems. This works describes the development of Artificial neural networks (ANN), Random Forests (RF), Support Vector Regression (SVR) and Extreme Gradient Boosting Machines (xgboost) using the same dataset of numerical samples used in the original works of Possidente et al. to predict the capacity of compressed members with angles (L), tee (T) or cruciform (X) sections for different lengths and section geometries. Then, the machine learning models are explained using a combination of domain knowledge inference, partial dependence plots and SHapley Additive exPlanations. The accuracy versus safety trade-off is discussed for a better-informed model selection. The accuracy of ML models is greater than the obtained with analytical methods, with the ANN being the best-fitting ML model for every section yielding a R2 above 0.9999, and the RF and SVR being too safe for some greater reduction factor values. These results show that ML models are capable of predicting the torsional or flexural-torsional buckling behaviour of compressed members and that can be used to design trusses or bracing systems composed of such elements.