Abstract: The element-free Galerkin method is applied to solve theincompressible viscous flows problem, which is described by the Navier-Stokesequation. The discrete formulation of the element-free Galerkin method is obtained bya weighted residual method, and the fractional step method in time domainis adopted. This method is useful because one may use the same movingleast-squares(MLS) interpolation functions for both velocity andpressure, and velocity and pressure are solved by independent equations,respectively. The Newton-Raphson iterative method is used for the velocity and pressure in each time step. Finally, the method is appliedto the shear-driver cavity flow to verify the validity and accuracyof this study.