This volume contains the proceedings of an international conference on Numerical Methods for Fluid Dynamics held at the University of Oxford in April 1995. Such conferences have been held at the Universities of Reading and Oxford since the early 1980s, under the auspices of the Institute for Computational Fluid Dynamics. The conferences have become regular and eagerly anticipated events in the CFD calendar, and attract a distinguished international group of speakers and delegates. The standard of papers is, as always, very high.The proceedings include work on all the latest current issues in CFD, and in particular are concerned with the analysis of CFD algorithms and their behaviour. The main themes of the present volume are algorithms and algorithmic needs arising from applications, Navier-Stokes on flexible grids, and environmental CFD. These proceedings begin with the 13 invited papers by eminent researchers, followed by the five papers by young researchers shortlisted for the Bill Morton prize (instigated at the conference), and finally include the 44 contributed papers.The distinguished group of invited speakers includes H Deconinck (VKI, Brussels), J C R Hunt (Meteorological Office), M A Leschziner (UMIST), D Mavriplis (ICASE). K W Morton (Oxford), K G Powell (Michigan), A Quarteroni (Milan), S Rill (Bremen), A N Staniforth (Quebec), N Stoufflet (Paris), J Thomas (NASA), N P Weatherill (Swansea), and P Wesseling (Delft).