JProgressBar not updating

Your showProgress method is being executed within the context of the Event Dispatching Thread. The EDT is responsible for, amongst other things, processing paint requests. This means that so long as your for-loop is executing, the EDT can not process any new paint requests (or handle the invokeLater events either) as it is blocking the EDT.

While there are any number of possible ways to solve the problem, based on your code example, the simplest would be to use a SwingWorker.

It has the capacity to allow your to execute the long running task the a background thread (freeing up the EDT), but also allows you means for publishing updates (if required) so that they can be processed in the EDT and also provides handy progress notification.

For example…

import java.awt.BorderLayout;
import java.awt.EventQueue;
import java.awt.GridBagConstraints;
import java.awt.GridBagLayout;
import java.awt.Insets;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.beans.PropertyChangeEvent;
import java.beans.PropertyChangeListener;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JProgressBar;
import javax.swing.SwingWorker;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
import javax.swing.border.EmptyBorder;

public class SwingWorkerProgress {

    public static void main(String[] args) {
        new SwingWorkerProgress();
    }

    public SwingWorkerProgress() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                try {
                    UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
                } catch (ClassNotFoundException | InstantiationException | IllegalAccessException | UnsupportedLookAndFeelException ex) {
                }

                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.setLayout(new BorderLayout());
                frame.add(new TestPane());
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }

    public class TestPane extends JPanel {

        private JProgressBar pbProgress;
        private JButton start;

        public TestPane() {

            setBorder(new EmptyBorder(10, 10, 10, 10));
            pbProgress = new JProgressBar();
            setLayout(new GridBagLayout());
            GridBagConstraints gbc = new GridBagConstraints();
            gbc.insets = new Insets(4, 4, 4, 4);
            gbc.gridx = 0;
            gbc.gridy = 0;
            add(pbProgress, gbc);

            start = new JButton("Start");
            gbc.gridy++;
            add(start, gbc);

            start.addActionListener(new ActionListener() {
                @Override
                public void actionPerformed(ActionEvent e) {
                    start.setEnabled(false);
                    ProgressWorker pw = new ProgressWorker();
                    pw.addPropertyChangeListener(new PropertyChangeListener() {

                        @Override
                        public void propertyChange(PropertyChangeEvent evt) {
                            String name = evt.getPropertyName();
                            if (name.equals("progress")) {
                                int progress = (int) evt.getNewValue();
                                pbProgress.setValue(progress);
                                repaint();
                            } else if (name.equals("state")) {
                                SwingWorker.StateValue state = (SwingWorker.StateValue) evt.getNewValue();
                                switch (state) {
                                    case DONE:
                                        start.setEnabled(true);
                                        break;
                                }
                            }
                        }

                    });
                    pw.execute();
                }
            });

        }
    }

    public class ProgressWorker extends SwingWorker<Object, Object> {

        @Override
        protected Object doInBackground() throws Exception {

            for (int i = 0; i < 100; i++) {        
                setProgress(i);
                try {
                    Thread.sleep(25);
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }

            return null;
        }
    }
}

Check out Concurrency in Swing for more details