The HAWC (High Altitude Water Cherenkov) gamma ray observatory has observed muons at nearly horizontal directions. The proximity of Sierra Negra and Pico de Orizaba volcanoes provides a range of depths with rock overburdens of up to approximately 30 km water equivalent. In the arrival directions not obstructed by the nearby volcanoes of Sierra Negra and Pico de Orizaba the depth traversed by muons is that of the Earth’s atmosphere for horizontal trajectories of approximately 0.2 km water equivalent. We have implemented a muon candidate selection procedure using line and plane finding algorithms to identify isolated muon tracks (lines) propagating near horizontally with the speed of light among a large background of extensive air shower (planes). This selection procedure also reconstructs the muon’s arrival direction. We have modified existing HAWC simulation software and developed geometry-based calculations to estimate detector acceptance and reconstruction resolution of arrival direction to determine the exposure as a function of rock overburden. Using this exposure and the rate of observed muons as a function of arrival direction we have performed a measurement of muon flux as a function of depth from 0.2 km water equivalent up to 30 km water equivalent. Muons that penetrate depths of greater than 3 km water equivalent are likely to have had initial energies in excess of 1 TeV. Our measurements are consistent with previous experiments that have observed high zenith angle (near horizontal) muon flux at or near sea level as well as muon flux measurements as a function of depth in deep underground facilities.