Hier ist ein Code-Snippet von Wikibooks

private static String longestCommonSubstring(String s1, String s2) {
    int start = 0;
    int max = 0;
    for (int i = 0; i < s1.length(); i++) {
        for (int j = 0; j < s2.length(); j++) {
            int x = 0;
            while (s1.charAt(i + x) == s2.charAt(j + x)) {
                x++;
                if (((i + x) >= s1.length()) || ((j + x) >= s2.length())) break;
            }
            if (x > max) {
                max = x;
                start = i;
            }
        }
    }
    return s1.substring(start, (start + max));
}