Fuzziness is a type of new incoherence. The fuzzy set theory is said to depict ambiguity.Fuzzy queuing model with flexible service policy is being investigated in this work. A parametric programming technique is designed to find the membership functions of queue length and sojourn time in steady state, in which the arrival rate and service rate are being pentagon fuzzy numbers. Based on  -cut approach and Zadeh’s extension principle, the fuzzy queues are transformed into family of crisp queues. The model’s potency is calculated for various possibilities of -cuts.