The present study involves computational investigation of effusion cooling over a flat plate through the different shaped holes. The interaction between the film jet and the mainstream flow creates a counter-rotating vortex pair, resulting jet detachment from the surface and insufficient film cooling coverage over the surface. To enhance the effusion cooling performance, shaped holes are used in place of standard cylindrical holes to reduce the effects of the counter-rotating vortex pair. Two different shaped holes i.e., conical-shaped and fan-shaped holes are used in the investigation and compared to the cylindrical holes. A commercial finite element method package COMSOL Multiphysics 5.5 is used to simulate and analyse the three-dimensional combustor liners of gas turbine. Data is presented for total 10 rows of effusion holes with injection angles 30o at blowing ratios 0.25, 1.0 and 3.2. The shaped holes provide better cooling effectiveness by increasing the lateral spread of coolant over the surface wall. The results show that both the shaped hole geometries can generate additional anti-counter rotating vortex pairs, which contribute to reducing the strength of the counter-rotating vortex pair. The coolant penetration and strong shear zones at the interaction of coolant jet and main stream in shaped holes are greatly reduced in comparison with cylindrical holes. For a low blowing ratio of 0.25, the conical-shaped holes exhibited adiabatic effectiveness that was 25% and 19% greater than the cylindrical and trapezoidal-shaped holes respectively. On the other hand, fan-shaped holes provide enhanced adiabatic effectiveness at increased blowing ratios. At higher value of blowing ratio 3.2, the adiabatic effectiveness increased by 13% compared to cylindrical holes and 4% compared to conical-shaped holes. In addition, velocity profiles and two-dimensional streamlines have been examined in order to study the flow be-havior on the surface.