In this paper we have considered a staggered cavity. It is equipped with purely viscous fluid. The physical design is controlled through mathematical formulation in terms of both the equation of continuity and equation of momentum along with boundary constraints. To be more specific, the Navier-Stokes equations for two dimensional Newtonian fluid flow in staggered enclosure is formulated and solved by well trusted method named finite element method. The novelty is increased by considering the motion of upper and lower walls of staggered cavity case-wise namely, in first case we consider that the upper wall of staggered cavity is moving and rest of walls are kept at zero velocity. In second case we consider that the upper and bottom walls are moving in a parallel way. Lastly, the upper and bottom walls are considered in an antiparallel direction. In all cases the deep analysis is performed and results are proposed by means of contour plots. The velocity components are explained by line graphs as well. The kinetic energy examination is reported for all cases. It is trusted that the findings reported in present pagination well serve as a helping source for the upcoming studies towards fluid flow in an enclosure domains being involved in an industrial areas.