Existing remote radioactive contamination depth estimation methods for buried radioactive wastes are either limited to less than 2 cm or are based on empirical models that require foreknowledge of the maximum penetrable depth of the contamination. These severely limits their usefulness in some real life subsurface contamination scenarios. Therefore, this work presents a novel remote depth estimation method that is based on an approximate three dimensional linear attenuation model that exploits the benefits of using multiple measurements obtained from the surface of the material in which the contamination is buried using a radiation detector. Simulation results showed that the proposed method is able to detect the depth of caesium-137 and cobalt-60 contamination buried up to 40 cm in both sand and concrete. Furthermore, results from experiments show that the method is able to detect the depth of caesium-137 contamination buried up to 12 cm in sand. The lower maximum depth recorded in the experiment is due to limitations in the detector and the low activity of the caesium-137 source used. Nevertheless, both results demonstrate the superior capability of the proposed method compared to existing methods.