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Numerical modeling of cylindrical semiconductor nano-lasers has been undertaken accommodating local gain variations in the active region of the device. Analysis is performed using both the cylindrical transfer matrix method and the finite element method. Calculations have thereby been performed of the modal gain and the lasing condition for the device. The model has been applied to annular active core structures and a comparison has been made of the requirements for achieving lasing via the excitation of TE01 and TM01 modes. For representative structures, it is shown that TE and TM mode lasing can be supported in devices having cavity lengths in the order of 1 and 60 μm, respectively.