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Theoretical calculations of threshold intensity and output frequency, as functions of magnetic field, are presented for the InSb spin-flip Raman laser (SFRL). These are based on a numerical solution of Maxwell's equations for the case of a pump beam of Gaussian profile, and various analytical results for more approximate models. The results are used to discuss nonlinear tuning characteristics, mode jumping, and the dependence of threshold power upon beam size. These are the first calculations to include the effects of finite beam size, which are found to be quite significant and consist chiefly of a marked asymmetry of the variation of threshold power and tuning rate across each mode. This asymmetry is in qualitative agreement with recent experimental observations. The model may be readily generalized to include higher modes and extended to the case of constant input power.