Ionizing-radiation-resistant bacteria (IRRB) could be used for bioremediation of radioactive wastes and in the therapeutic industry. Limited computational works are available for the prediction of bacterial ionizing radiation resistance (IRR). In this work, we present ABClass, an in silico approach that predicts if an unknown bacterium belongs to IRRB or ionizing-radiation-sensitive bacteria (IRSB). This approach is based on a multiple instance learning (MIL) formulation of the IRR prediction problem. It takes into account the relation between semantically related instances across bags. In ABClass, a preprocessing step is performed in order to extract substructures/motifs from each set of related sequences. These motifs are then used as attributes to construct a vector representation for each set of sequences. In order to compute partial prediction results, a discriminative classifier is applied to each sequence of the unknown bag and its correspondent related sequences in the learning dataset. Finally, an aggregation method is applied to generate the final result. The algorithm provides good overall accuracy rates. ABClass can be downloaded at the following link: http://homepages.loria.fr/SAridhi/software/MIL/.