Assuming you are using DefaultTableModel as table model, this should be enough:
int[] viewIndexes = table.table.getSelectedRows();
for(int i = viewIndexes.length - 1; i >= 0; i-- ) {
int modelIndex = table.convertRowIndexToModel(viewIndexes[i]);
((DefaultTableModel)table.getModel()).removeRow(modelIndex);
}
Never forget to convert the selected indexes from view to model. Otherwise you'll have problems if your table is sorted.
If you are using a custom TableModel, the process is almost the same, there won't be great differences.
In addition, you don't have to do nothing to update the view after adding/deleting/updating data, the model will notify the view in such events and this last one will be updated accordingly.
See How to use Tables tutorial for further details.