To show a modal dialog box in an Android application using Java, you can follow these steps:

1. Create a layout file for your dialog box. For example, create a file called dialog_layout.xml in the res/layout directory with the following content:

   <LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
       android:layout_width="match_parent"
       android:layout_height="wrap_content"
       android:orientation="vertical">

       <!-- Add your dialog box content here -->

   </LinearLayout>

Customize the layout according to your dialog box requirements.

2. In your activity or fragment, create a method to show the dialog box:

   import android.app.Dialog;
   import android.os.Bundle;
   import android.view.LayoutInflater;
   import android.view.View;

   public class YourActivity extends AppCompatActivity {

       // Declare a variable to hold the dialog
       private Dialog dialog;

       // Method to show the dialog box
       private void showDialog() {
           // Create an instance of the dialog
           dialog = new Dialog(this);

           // Set the content view by inflating the layout
           LayoutInflater inflater = LayoutInflater.from(this);
           View dialogView = inflater.inflate(R.layout.dialog_layout, null);
           dialog.setContentView(dialogView);

           // Optionally, customize the dialog properties
           dialog.setTitle("My Dialog");
           dialog.setCancelable(false);

           // Show the dialog
           dialog.show();
       }

       // Additional code for your activity or fragment
       // ...
   }

In this example, the showDialog method creates an instance of the Dialog class. The layout for the dialog box is inflated using the LayoutInflater, and the content view of the dialog is set using dialog.setContentView. You can customize the dialog properties, such as title and cancelability, according to your requirements. Finally, dialog.show() is called to display the dialog box.

3. Call the showDialog method when you want to show the dialog box. For example, you can call it from a button click listener:

   Button showDialogButton = findViewById(R.id.show_dialog_button);
   showDialogButton.setOnClickListener(new View.OnClickListener() {
       @Override
       public void onClick(View v) {
           showDialog();
       }
   });

In this example, a button with the ID show_dialog_button is defined in your activity layout. The setOnClickListener method is used to set a click listener on the button, and the showDialog method is called when the button is clicked.

Make sure to adjust the code according to your specific application structure and requirements. You can further customize the dialog box layout and behavior by adding buttons, text views, or other UI components to the dialog layout file, and handling their interactions within your activity or fragment.