We have developed an efficient method to assess the stability of linear time-invariant (LTI) systems and continuous-time nonlinear systems. It is based on the modulus of the spectral radius of a particular matrix transformation of the original system state matrix, in the case of LTI systems, or the Jacobian for nonlinear systems. The iterated Shanks transformation is applied to Gelfand’s formula to improve the computational speed for obtaining the aforementioned spectral radius. Advantageously, our stability criterion does not rely on the system’s characteristic equation. Furthermore, it obviates the need for calculating all the eigenvalues of the system. Several examples, including a fluidized bed reactor, a CSTR, and a hypothetical 20th-order system, are presented for illustration. A CPU-time analysis is provided, and it is demonstrated that our method is several orders of magnitude computationally faster than the classical Routh-Hurwitz stability test for systems with dimensions from two up to 80.