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A two dimensional incompressible viscous laminar flow past rectangular cylinder was studied numerically. The simulations were done using modified MAC algorithm on the basis of finite difference approach and validated with literature results. Affect of wing thickness was analyzed for oscillating rectangular cylinder in sinusoidal plunging motion. The incompressible viscous laminar flow was simulated using in-house code for the given range of ct. Non-inertial reference frame approach was implemented and validated for square cylinder with available literature. Thin section showed good aerodynamic efficiencies. Individually, all thickness ratios of rectangular cylinder showed potential for Insect flight modeling along with other applications in the fields of aerospace, civil and coastal engineering as Flow control, enhanced dissipation and flow mixing phenomenon. Further, two dimensional wing in sinusoidal plunging was carried out to examine the effect of its cross - sectional shape.The flat plate under sinusoidal plunge motion is compared with a corrugated, elliptical and NACA. Overall NACA airfoil is showing better performance characteristics compared with other shapes.