Stackelberg games with simple recourses are formulated, in which the coefficients of equality constraints are represented as continuous type fuzzy random variables or discrete type ones. In general, these problems cannot be solved by applying the conventional methods, since simple recourses involving fuzzy random variables have not been defined. To cope with such fuzzy random variables, a possibility measure concept is applied. Then, two kinds of Stackelberg games with simple recourses are converted into usual optimization problems for some fixed degrees of permissible possibility levels specified by the first level’s player. For the transformed optimization problems, the Stackelberg solution concept of the first level’s player is introduced. By using an example, the property of the proposed Stackelberg solution concept is explained.