Based on the concept of the folding, the folding in X-direction and in Y-direction are defined and denoted by the X-Folding and the Y-Folding respectively. We consider a random variable X which follows a rectangular distribution "R(a, b) distribution" with two parameters a, b. This paper aims to apply the folding on the unit area P($a{leq}X{leq}b$) and also to study the proposed folding in each direction for R(a, b) distribution and the generated family of the corresponding constructed rectangular probability distributions. Some main properties of this family are reviewed. According to the proposed folding, we derive and discuss some important corresponding functions in closed forms.