Bearing elements are widely used in rotating machines and their failure results in a considerable amount of downtime of the machines. The aim of this work is to classify defects in a bearing. Three types of classification have been done: (i) Binary classification: classification as non-defective or defective bearing, (ii) 3-class classification such as non-defective, defective with inner ring defect and defective with roller defect and finally (iii) 7-class classification corresponding to no defect condition, three ring defect conditions pertaining to indentations of three different sizes on the inner ring and three roller defect conditions corresponding to indentations of three different sizes on the roller. The open-access data generated using a rolling bearing test rig from the Politecnico Di Torino, Italy, has been used for this work. The data had been obtained using 2 accelerometers on two bearing housings for multiple load and speed combinations. For classification, in the present work, classical ML algorithms such as logistic regression (LR), K-Nearest Neighbour (K-NN) classification algorithm, random forest (RF), support vector classifier (SVC) and kernel support vector machine (KSVM) have been used. All these techniques gave very promising results, the classification accuracy varying from 0.7969 to 0.9996 for all speed-load conditions. Such classification work across multiple operational conditions, with multiple fault conditions and multiple signatures with faulty components, has not been reported.