Tumors in portions of a subject's body that have a longitudinal axis (e.g., the torso, head, and arm) can be treated with TTFields by affixing first and second sets of electrodes at respective positions that are longitudinally prior to and subsequent to a target region. An AC voltage with a frequency of 100-500 kHz is applied between these sets of electrodes. This imposes an AC electric field with field lines that run through the target region longitudinally. The field strength is at least 1 V/cm in at least a portion of the target region. In some embodiments, this approach is combined with the application of AC electric fields through the target region in a lateral direction (e.g., front to back and/or side to side) in order to apply AC electric fields with different orientations to the target region.