This article presents an active-sensing strategy based on frontier exploration to enable the autonomous reconstruction of the geometry of a metal surface by a mobile robot relying on ultrasonic echoes. Such a strategy can be beneficial to the development of a fully autonomous robotic agent for the inspection of large metal structures such as storage tanks or ship hulls. The developed method relies on a grid map generated by detecting the first echo within the measurements referring to the closest edge to the sensor, and it employs a utility function that we define to balance travel cost and information gain using an estimation of the plate geometry obtained via beamforming. Next, the sensor is directed to the next best location. The developed method is evaluated in simulation and compared with multiple algorithms, essentially closest and random frontier point selection. Finally, an experiment using a mobile robot equipped with co-localized pair of transducers is used to validate the viability of the approach.