A Reynolds-type equation for finite hydrodynamic bearings, (plane slid
er and cylindrical journal), with rough surfaces (longitudinal, transv
erse and isotropic roughnesses), has been solved using the stochastic
finite element method considering film thickness to be a stationary, e
rgodic stochastic process with mean zero. Mean steady-state characteri
stics have been obtained and compared with those obtained by previous
investigators. The effect of a spatially randomly varying component of
roughness has been studied by giving different input standard deviati
ons of film thickness and calculating output standard deviation of max
imum pressure for different scales of fluctuation using the first-orde
r second-moment method.