An algorithm to simulate steady, viscous free surface flows is presented in this paper. A Picard-type approach wherein the flow and free surface updates are performed alternately is utilized to iterate for a solution. The procedurr is intended for large-scale two-or three-dimensional problems. A surface-intinsic coordinate system which facilities representation of gencral ike surface shapes is used. Using a Galerkin finite element method (GFEM), two free surface updates, namely kinematic and n o d stress updates arc formulated. It is shown that the effects of surface tension, surface tension gradients and imposition of contact angles can be simulated elegantly within the h e w o r k of the GFEM. A novel feature of the updates is that the d e f o d o n s arc sought in a direction n o d to the cumnt itaate free surface shape, with the d t that the method is ideally suited when used in conjunction with an automatic mcsh generator. With the normal stress updatc a volume constraint can also be imposed. A -&xi method is utilized to solve iteratively one degree of freoQom at a time for the solution of the flow variabks. As a resulf the memory and disc space requirCments are minimal. Sample problems in extrusion, coating and crystal growth are presented to clearly illustrate the convergence behaviour and accuracy of thc algorithm.