The High Altitude Water Cherenkov (HAWC) observatory is an array of large water Cherenkov detectors sensitive to gamma rays and hadronic cosmic rays in the energy band between 100 GeV and 100 TeV. The observatory will be used to measure high-energy protons and cosmic rays via detection of the energetic secondary particles reaching the ground when one of these particles interacts in the atmosphere above the detector. HAWC is under construction at a site 4100 meters above sea level on the northern slope of the volcano Sierra Negra, which is located in central Mexico at 19 N latitude. It is scheduled for completion in 2014. In this paper we estimate the sensitivity of the HAWC instrument to point-like and extended sources of gamma rays. The source fluxes are modeled using both unbroken power laws and power laws with exponential cutoffs. HAWC, in one year, is sensitive to point sources with integral power-law spectra as low as 5×10-13 cm-2sec-1 above 2 TeV (approximately 50 mCrab) over 5 sr of the sky. This is a conservative estimate based on simple event parameters and is expected to improve as the data analysis techniques are refined. We discuss known TeV sources and the scientific contributions that HAWC can make to our understanding of particle acceleration in these sources. © 2013 Elsevier B.V. All rights reserved.