.modal {
    bottom: 0;
    display: none;
    left: 0;
    overflow-x: auto;
    overflow-y: scroll; /* <--- this guy right here */
    position: fixed;
    right: 0;
    top: 0;
    z-index: 1040;
}

明确地将overflow属性设置为scroll将导致浏览器显示滚动条是否有溢出.