A new algorithm is presented for simulating stable random variables on a digital computer for arbitrary characteristic exponent α(0 < α ≤ 2) and skewness parameter β(-1 ≤ β ≤ 1). The algorithm involves a nonlinear transformation of two independent uniform random variables into one stable random variable. This stable random variable is a continuous function of each of the uniform random variables, and of α and a modified skewness parameter β' throughout their respective permissible ranges.