We present the B'ezier extraction operator and isogeometric Bézier elements for non-uniform rational B-Spline (NURBS)-based isogeometric analysis. The Bézier extraction operator allows numerical integration of smooth functions to be performed on C0 Bézier elements. We show how the Bézier extraction operator is computed for NURBS. We then show that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays. All significant changes may be implemented in a shape function subroutine. Copyright © 2010 John Wiley & Sons, Ltd.