There is provided an elongate aerosol-generating device having at least a portion of its transverse external cross-section defined by a shape having at least five sides. The shape may be polygonal. The cross-sectional shape of the device confers stability against rolling. The elongate aerosol-generating device includes a substrate receiving cavity configured to receive an aerosol-forming substrate to form an aerosol, a heating element, and a power supply configured to provide power to the heating element. The external shape of the aerosol-generating device may be defined by a housing having at least two separable portions. The external shape may be defined by a polygon having convexly curved faces to minimize perceived misalignments between adjacent housing portions.