A class of stochastic linear programs termed stable stochastic linear programs defined in terms fo convergence of sequences of stochastic linear program is introduced. A sufficient regularity condition for such stability is given, slightly stronger than the necessary and sufficient condition that a stochastic linear program (SLP) has optimal value. This is a minimal condition in a certain sense. Applications of this regularity condition to Monte Carlo methods, numerical solution of the distribution problem and two-stage programming are given.