A spatial linear stability analysis of circular and elliptical jets has been carried out. For the circular jet, the Michalke's shooting method has been extended to the case with a swirling basic flow. For the elliptical jet, an algebraic eigenvalue problem has been formulated by applying the Chebyshev and Fourier spectral collocation method to the disturbance equations of the flow expressed in a generalized cylindrical coordinate system. The resulting algebraic eigenvalue problem was solved using the inverse power method. The approach developed is capable of handling the influences of different distributions of the momentum thickness, swirl, and heat release. In addition to studying the stability properties of the elliptical jet in comparison with those of a circular jet, the linear stability analysis has been used to obtain the insight into the entrainment process. A possible way to enhance the entrainment of elliptical jets has been suggested.