SUNSPOTS are areas of cooler gas and stronger magnetic fields in the Sun’s photosphere (its ’surface’), but just how they form and are maintained has long been a puzzle. It has been proposed(1) that small vertical magnetic flux tubes, generated deep within the Sun, develop downflows around them when they emerge at the surface. The downflows bring together a large number of flux tubes in a cluster to form a sunspot, which behaves as a single flux bundle as long as the downflows bind the flux tubes together. Until now, however, it has not been possible to test this model with subsurface observations. Here we use the recently developed technique of travel time helioseismology(2) to detect the presence of strong downflows beneath both sunspots and the bright features known as plages. The flows have a velocity of similar to 2 km s(-1), and they persist to a depth of about 2,000 km. The data suggest, however, that the vertical magnetic field can be a coherent Bur bundle only to a depth of similar to 600 km; below this depth it is possible that the downflows hold together a loose collection of flux tubes to maintain the sunspots that we see.