How to remove UL class in wp_nav_menu?

To remove ul class from wp_nav_menu, you will have to define menu_class to false. Default wp_nav_menu ul menu class is menu.

<?php wp_nav_menu( array( 'container' => false, 'items_wrap' => '<ul>%3$s</ul>', 'theme_location' => 'mainmenu' ) ); ?>

I added mainmenu as theme_location. You should change it to your theme location.

Read full list of args on wp_nav_menu codex page.

EDIT:

To remove id and classes from ul menu you can define your menu like this.

'container' => false,
'items_wrap' => '<ul>%3$s</ul>'

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