Abstract: A least-square point collocation meshless formula based on kernel reproducing is proposed to discretize nonlinear partial differential equations for two-dimensional incompressible viscous hydrodynamic problems. A two-dimensional Stokes problem, Couette flow, is taken as a typical example to verify the validity of this meshless approach. The distributions of velocity for the Couette flow are investigated for positive and negative gradient pressures, respectively. The Couette flows with these types of pressure gradients are significant in the lubrication theory. The viscous fluid flow film formed in the journal bearing has similar flow property as that of the Couette flow. The numerical example shows that results obtained in this meshless approach are highly accurate for both uniform and random distribution of discretized points.