Incompressible laminar flow in a square cavity is studied numerically for various values of Reynolds number. The classical Lid-Driven cavity problem has been solved in three methods (Vorticity-Stream function formulation method, Projection Method or Marker and Cell (MAC) Method and Projection technique with Runge-Kutta fourth order method (MAC-RK4)). The uniform fine grid is used in finite difference approximation and the implemented explicit time integration MATLAB code is validated with benchmark results. In the present work, staggered and collocated grid arrangement along with various sizes of uniform structured Cartesian grid was used. We extend these methods to study the flow patterns in square, triangular and trapezoidal enclosure. In addition we tested the accuracy of present numerical computational methods. © 2020 Author(s).