In this chapter, we propose the concepts of flexible numbersFlexible number, flexible-numbered vectorsFlexible-numbered vector, and flexible vectorsFlexible vector based on flexible linguistic valuesFlexible linguistic value and flexible setsFlexible set; give their definitions and representations; and analyze their geometric characteristics. Further, we define the arithmetic operations, scalar multiplication, and exponentiation of flexible numbersFlexible number; define the addition and scalar multiplication of flexible vectorsFlexible vector; and point out the properties of these operations. Then, on the bases of flexible numbersFlexible number and flexible linguistic functionsFlexible linguistic function, we propose the concept of flexible functions, give their definitions and types, analyze their analytic expressions, and further discuss the flexible-vector functionsFlexible-vector function.