When empirical data correspond to a simple decay or growth process, or to a combination of these both processes, it is possible to approximate these data curve with a finite exponential senes by Prony's method. This paper describes the numerical treatment of the Endochronic constitutive theory for soils which is the hereditary integral in form, and the method of the representation of finite exponential series of the integral kernel. Some examples of the approximation by finite exponential series for the error function and the normalized incomplete gamma function are given by means of Prony's method.