The objective of this research is to study the ability of a meshless method, called finite point method, in solving incompressible fluid flow problems using two stabilization schemes. The main goal of meshless methods is to reduce or remove the cost of grid generation. This issue is implemented using the satisfaction of governing differential equations on a regular or irregular set of nodes by interpolation functions, based on special least-squares approximations. In this research, the finite point method is used to solve the Stokes and the Navier-Stokes equations by employing two different stabilization schemes. In addition, the effects of least-squares approximations are studied.