Microstrip antennas are popular for their conformability on non-planar mounting surfaces. A Plethora of investigations is present in the open literature. However, the main focus of those contributions has been on convex structured conformal antennas. In this work, we take the opportunity to investigate on concave microstrip antenna. In this work, a rectangular microstrip antenna on a concave cylindrical surface is designed and simulated using commercially popular 3D EM software HFSS. Input impedance, reflection coefficient, and radiation patterns are also shown here. The antenna is designed for GSM-band applications. Finally, the effect of different curvatures on the radiation pattern is presented.