Experimental and theoretical studies have established that the transition to turbulent from laminar flow (promoting the drag coefficient) may be prevented/delayed by the fluid suction from the boundary layer to the plate. Due to such an active role of laminar flow control in plummeting drag ensuing improvement in the power of vehicle by a considerable amount, this work aims to analyze periodic suction impact on 3-dimensional unsteady oscillatory flow of Jeffery fluid flowing laminarly along an infinite porous plate lying horizontally with transverse sinusoidal suction. The free stream velocity swings to and fro about a constant mean in time. The flow becomes 3-dimensional because of transverse direction of the periodic suction velocity. Approximate solutions are attained for velocity components, shear stresses and pressure. On these physical quantities the impact of dimensionless parameters budding in the problem under consideration are graphically visualized and analytically conferred. The x-component of velocity is noted to be increasing for rising values of Re which causes the decay in boundary layer thickness. Further, the velocity component u is found to be reducing with increasing values of β because of the fluid thickening. It is also observed that an enhancement in Re causes to reduce the pressure. On the contrary, α causes to rise the pressure. The shear stress along the z-direction is augmented by increasing the suction parameter. The shear stress in the z-direction also increases by increasing the elastic parameter because of the thickening of the fluid. The results of present study agree to published work in limiting sense. This study is advantageous in manufacturing and designing LFCS (laminar flow control system) to improve the vehicle power necessity.