An elongate aerosol-generating device (100, 1000) has at least a portion of its transverse external cross-section defined by a shape having at least 5 sides. The shape may be polygonal. The cross-sectional shape of the device confers stability against rolling. The elongate aerosol-generating device may comprise a substrate receiving cavity (302) adapted to receive an aerosol-forming substrate to form an aerosol, a heating element, and a power supply (506) adapted to provide power to the heating element. In some embodiments the external shape of the aerosol-generating device may be defined by a housing having at least two separable portions. In some embodiments the external shape may be defined by a polygon having convexly curved faces to minimise perceived misalignments between adjacent housing portions.