AbstractSuppose sensors are deployed randomly in a long thin strip, and suppose each sensor can detect objects within a fixed distance. We say that the sensors achieve barrier coverage if there is no path across the strip that a small object can follow that avoids detection by the sensors. We give fairly precise results on the probability that barrier coverage is achieved as a function of the range of the sensors, the height and length of the strip, and the number of sensors deployed. In particular, we show that the most likely obstruction—a rectangular region crossing the strip which is devoid of sensors—does not in general dominate the probability of failure of barrier coverage. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 429–478, 2016