The problem of stealthy sensor attacks for labeled Petri nets is considered. An operator observes the plant to establish if a set of critical markings has been reached. The attacker can corrupt the sensor channels that transmit the sensor readings, making the operator incapable to establish when a critical marking is reached. We first construct the stealthy attack Petri net that keeps into account the real plant evolutions observed by the attacker and the corrupted plant evolutions observed by the operator. Starting from the reachability graph of the stealthy attack Petri net, an attack structure is defined: it describes all possible attacks. The supremal stealthy attack substructure can be obtained by appropriately trimming the attack structure. An attack function is effective if the supremal stealthy attack substructure contains a state whose first element is a critical marking and the second element is a noncritical marking
