Transport phenomena in periodically driven cavities are important because of their relevance in polymer processing and microfluidics. The transient periodic flow of viscoelastic fluids in a cuboidal cavity, with periodic motion of top plate, was studied in this work. Flow with a characteristic time scale was achieved through the simple harmonic motion of the top plate. The flow in the cavity was characterized by measuring planar velocity fields using particle image velocimetry (PIV). Temporal variation of velocity except at central vertical plane showed predominance of the plate frequency. The temporal point variations, though seemingly similar to those for Newtonian and purely viscous non-Newtonian fluids, led to rich varieties of spatial flow structures in case of the viscoelastic fluids. The overall flow behavior was characterized using spatial variations, phase trajectories, and streamline patterns. The transition from low Reynolds number steady-lid driven type flow to complex vortical patterned flow was observed during a cycle of periodic motion of viscoelastic fluids. The effects of elasticity and inertia on the flow fields were analyzed. Computational fluid dynamics simulations with purely viscous shear thinning fluid (power law) and Newtonian fluid showed significant differences with experimental measurements on viscoelastic fluids.