The search for habitable exoplanets received new momentum with recent discoveries of tens of exoplanets in habitable zones around cool stars. Many of host stars are represented by active M dwarfs and young G and K dwarfs generating intense X-ray and Extreme UV (XUV) radiation fluxes from their quiescent coronae and intense and frequent flares. This suggests that many of rocky exoplanets are exposed to large fluxes (100-300) of stellar XUV radiation that are by a factor of 30-300 greater than that received by our planet today. The stellar XUV fluxes ionize and heat the upper atmospheres of exoplanets, driving significant atmospheric escape via hydrodynamic escape of both ions and neutrals. Here, we present the results of application of the One-Dimensional (1-D) Global Ionosphere Thermosphere Model (GITM) to an Earth-like planet exposed to 1, 10 and 60 times XUV fluxes of the current Earth. The results suggest the upper atmospheric mass loss is dominated by oxygen and nitrogen ion escape between XUV fluxes of 1-10 XUVEarth, while the planetary atmosphere transitions to a hydrodynamic escape state at the XUV flux of ~60 XUVEarth. We present the thermodynamic atmospheric parameters and total atmospheric escape rates for unmagnetized and magnetized Earth-like planets for parameter regimes relevant to the ongoing search for spectral signatures of escape processes that could impact the atmospheric evolution of rocky planets and their potential habitability.