Abstract: This paper introduces the application of a rational and indicial function in the time-domain simulation of bridge deck self-excited aerodynamic forces. The limiting and transient characteristics of both expressions are analyzed and compared. Theoretical analysis and numerical results indicate that the limiting characteristics of the indicial function, independent on the identified parameters, are in consistent with the quasi-steady wind-load characteristics. Thus, the indicial-function-expressed self-excited force model is a unification of two models: the self-excited aerodynamic forces expressed with flutter derivatives and the quasi-steady wind loads described with aerostatic load coefficients. It is this kind of unification that makes the indicial functions capable of the analyzing of wind-structure interaction with nonzero mean response values, such as the case where the effects of mean wind loads are included. In contrast with the indicial functions, limiting characteristics of the rational functions are completely dependent upon the parameters identified and not in consistent with the quasi-steady wind-load characteristics. As a result, its application should be limited within cases with zero mean values of vibration. A method is presented in this paper to meet such shortcomings of the rational functions which compels equivalence between some parameters and the quasi-steady wind-load characteristics. The transient characteristics of both the indicial function and rational function, which depend upon the identified parameters, are mere numerical results and may not represent the real transient aerodynamic characteristics of bridge decks. This is due to only the spectrum equivalence of self-excited forces, which does not include transient characteristics, is involved in the identification of function parameters. Consequently, very high transient values and time-consuming attenuating process may be formed, which result in long-playing distorted simulation of self-excited aerodynamic forces during the time-domain analysis of a wind-structure interaction. An effective measure, which may overcome this phenomenon by predefining numerical range for exponential parameters, is available in this literature.