This paper describes the formulation of shape functions and their derivatives for universal serendipity elements in finite element analysis, which allows for flexibility in locating edge nodes. Universal serendipity elements are defined as isoparametric elements having linear, quadratic and cubic node configurations at their edges in an arbitrary manner. Edge nodes positioned at the same relative distance from corner nodes in both master element and physical element provide improved accuracy over nodes positioned locally without regard for the global configuration. The nea formulation allows the user to change the order of elements in a very simple manner and also provides accurate solutions for nodal positions, which are not allowed using the standard elements. (C) 1999 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved.