CSS div element - how to show horizontal scroll bars only?

You shouldn't get both horizontal and vertical scrollbars unless you make the content large enough to require them.

However you typically do in IE due to a bug. Check in other browsers (Firefox etc.) to find out whether it is in fact only IE that is doing it.

IE6-7 (amongst other browsers) supports the proposed CSS3 extension to set scrollbars independently, which you could use to suppress the vertical scrollbar:

overflow: auto;
overflow-y: hidden;

You may also need to add for IE8:

-ms-overflow-y: hidden;

as Microsoft are threatening to move all pre-CR-standard properties into their own ‘-ms’ box in IE8 Standards Mode. (This would have made sense if they'd always done it that way, but is rather an inconvenience for everyone now.)

On the other hand it's entirely possible IE8 will have fixed the bug anyway.

This solution is without height/width specification for the father div so it will be responsive to window resizing and most useful cause horizontal scrollbars appears just if needed.

.container{
    padding:20px;
    border:dotted 1px;
    white-space:nowrap;
    overflow-x:auto;
}

.box{
    width:100px;
    height:180px;
    background-color: red;
    margin:10px;
    display:inline-block
}

Take a look at DEMO

I also had to add white-space: nowrap; to the style, otherwise elements would wrap down into the area that we're removing the ability to scroll to.