This paper aim to develop a two-dimensional computational model to study the fluid dynamic behaviour in a square cavity driven by an oscillating lid using staggered grid based finite volume method. Firstly the developed computational model is validated with that of other researcher’s results for the case of finite wall motion. Later the numerical simulations are performed for the case of top wall oscillations for various combinations of Reynolds number and frequencies. From these simulations an optimum frequency is chosen and then with the optimum frequency the simulations are carried out to explore the vortex behaviour for the cases of parallel wall oscillations (both top and bottom walls moving in the same direction) and anti-parallel wall oscillations (both top and bottom walls moving in the opposite direction). From these simulations it may be concluded that Re = 1000 is medium range of operation for better mixing inside the cavity for the cases of parallel and anti-parallel wall oscillations. Keywords: Finite volume method, First order upwind scheme, Oscillating lid driven cavity, Simple algorithm