A new class of all-fiber beam shaping devices has been realized by inverse etching the end face of single mode and multimode fibers to form a concave cone tip. Concave tip fiber can convert a Gaussian beam profile to a flat top beam profile with a uniform intensity distribution. A flat top beam with intensity variation of approx. 5% and flat top diameter to spot diameter ratio of 67% has been achieved. This device can also change the beam shape from a Gaussian to a donut by moving the observation plane. A flat top multimode fiber beam delivery is attractive for applications which require high power and uniform intensity distribution. In single mode fiber, concave tips could be used to reduce the beam spot size diameter, enabling efficient light coupling from a single mode fiber to an integrated optical waveguide.