The current work is concerned with studying the effects of rational-function approximation (RFA) coefficients used to represent the unsteady aerodynamics based on computational fluid dynamics (CFD) results on the transonic aeroelastic stability analyses. The CFD calculations are based on the Euler equations, and the code uses a finite volume formulation for general unstructured grids. A centered spatial discretization with added artificial dissipation is used, and an explicit Runge-Kutta time marching method is employed. The dynamic system considered in the present work is a NACA 0012 airfoil-based typical section in the transonic regime. Unsteady calculations are performed for mode-by-mode and simultaneous excitation approaches, the latter defined by orthogonal Walsh functions. A technique based on power spectral density (PSD) is employed to allow the splitting of the aerodynamic coefficient time histories into the contribution of each individual mode to the corresponding aerodynamic transfer functions. Generalized unsteady aerodynamic forces are approximated by a rational function in the Laplace domain, in which nonlinear parameters are selected through a non-gradient optimization process. Results indicate that small variations in the aerodynamic lag states that compose the rational-function approximation considerably impact the flutter onset point identification in frequency-domain aeroelastic stability analyses.