The closure of the set of the expansions of real numbers of [0, 1] is a subshift of a ∈ ℕ a < β ^ℕ, called the beta-shift. This dynamical system is characterized by the beta-expansion of 1; in particular, it is of finite type if and only if d _β(1) is finite; β is then called a simple beta-number.

We first compute the beta-expansion of 1 for any cubic Pisot number. Next we show that cubic simple beta-numbers are Pisot numbers.