JxBrowser DOM API allows working with HTML SELECT and OPTION elements. To work with SELECT element, the DOMSelectElement class is used. Let's see how to access SELECT element on web page that contains the following HTML code: 

<select id='select-tag'>
  <option value="volvo">Volvo</option>
  <option value="saab">Saab</option>
  <option value="mercedes">Mercedes</option>
  <option value="audi">Audi</option>
</select>

To access SELECT element use the following JxBrowser API: 

DOMDocument document = browser.getDocument();
DOMSelectElement select = (DOMSelectElement) document.findElement(By.id("select-tag"));

Now, using the select instance you can get information about its options, programmatically select specified option. For example: 

List<DOMOptionElement> options = select.getOptions();
options.get(2).setSelected(true);

The complete sample you can find below: 

import com.teamdev.jxbrowser.chromium.Browser;
import com.teamdev.jxbrowser.chromium.dom.By;
import com.teamdev.jxbrowser.chromium.dom.DOMDocument;
import com.teamdev.jxbrowser.chromium.dom.DOMOptionElement;
import com.teamdev.jxbrowser.chromium.dom.DOMSelectElement;
import com.teamdev.jxbrowser.chromium.events.FinishLoadingEvent;
import com.teamdev.jxbrowser.chromium.events.LoadAdapter;
import com.teamdev.jxbrowser.chromium.swing.BrowserView;

import javax.swing.*;
import java.awt.*;
import java.util.List;

/**
 * The sample demonstrates how to programatically select an option item in SELECT tag.
 */
public class DOMSelectOptionSample {
    public static void main(String[] args) {
        Browser browser = new Browser();
        BrowserView browserView = new BrowserView(browser);

        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
        frame.add(browserView, BorderLayout.CENTER);
        frame.setSize(700, 500);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);

        browser.addLoadListener(new LoadAdapter() {
            @Override
            public void onFinishLoadingFrame(FinishLoadingEvent event) {
                if (event.isMainFrame()) {
                    Browser browser = event.getBrowser();
                    DOMDocument document = browser.getDocument();
                    DOMSelectElement select = (DOMSelectElement) document.findElement(By.id("select-tag"));
                    selectOptionByIndex(select, 2);
                }
            }
        });
        browser.loadHTML("<html><body><select id='select-tag'>\n" +
                "  <option value=\"volvo\">Volvo</option>\n" +
                "  <option value=\"saab\">Saab</option>\n" +
                "  <option value=\"opel\">Opel</option>\n" +
                "  <option value=\"audi\">Audi</option>\n" +
                "</select></body></html>");
    }

    private static void selectOptionByIndex(DOMSelectElement select, int index) {
        List<DOMOptionElement> options = select.getOptions();
        options.get(2).setSelected(true);
    }
}