The High Altitude Water Cherenkov (HAWC) observatory is an array oflarge water Cherenkov detectors sensitive to gamma rays and hadronic cosmicrays in the energy band between 100 GeV and 100 TeV. The observatory willbe used to measure high-energy protons and cosmic rays via detection of theenergetic secondary particles reaching the ground when one of these particlesinteracts in the atmosphere above the detector. HAWC is under constructionat a site 4100 meters above sea level on the northern slope of the volcano SierraNegra, which is located in central Mexico at 19ºN latitude. It is scheduledfor completion in 2014. In this paper we estimate the sensitivity of the HAWCinstrument to point-like and extended sources of gamma rays. The source fluxesare modeled using both unbroken power laws and power laws with exponentialcutoffs. HAWC, in one year, is sensitive to point sources with integral power-lawspectra as low as 5 × 10⁻¹³ cm⁻² sec⁻¹ above 2 TeV (approximately 50mCrab) over 5 sr of the sky. This is a conservative estimate based on simpleevent parameters and is expected to improve as the data analysis techniquesare refined. We discuss known TeV sources and the scientific contributions that HAWC can make to our understanding of particle acceleration in these sources.