The authors describe a numerical procedure for the solution of the problem of hydro-dynamic lubrication in the hydrostatic extrusion process. The lubricant is assumed to be a Newtonian fluid and in this preliminary analysis it is assumed that the yield strength of the worked material remains constant. Elastic deformation of the billet as it enters and leaves the die is considered but this effect is found to have only a small influence upon the thickness of the lubricant film which is generated. Thermal effects arising from plastic deformation of the billet and viscous dissipation in the lubricant film are also considered. Theoretical results are presented showing the influence of die angle and reduction ratio upon values of film thickness and extrusion pressure for two materials.