For numerical simulations, we will use finite difference approximation to solve non-dimensional Navier-Stokes equations (NSEs) which has forms stream functions and vorticity. The fluid flow inside T - shaped cavity is movement subject to laminar flow. The equations of motion and energy of the viscous fluid flow apply for a steady state of incompressible fluids. The fluid mechanics under this boundary is simulated in two dimensional domains" x and y". Under these boundary conditions we simulate the streamlines, vorticity, temperature distribution and velocity vector in x-y plane. The head part of the cavity is driven by the horizontal velocity in x-direction. During the motion of the fluid inside the cavity, some vertices vorticity will appear, these vertices indicate that position and change its positions under changing the Reynolds numbers. The viscous fluid motion is simulated under the Prandtl number is equal 1.96 and the Reynolds numbers 1, 50, 100, 150 and increasing the Reynolds number by interval 50 and the maximum Reynolds number is 2000.