Flexible manipulator systems exhibit many advantages over their traditional (rigid) counterparts. However, they have not been favored in production industries due to its obvious disadvantages in controlling the manipulator. This paper presents theoretical investigation into the dynamic modeling and characterization of a constrained two-link flexible manipulator, by using finite element method. The final derived model of the system is simulated to investigate the behavior of the system. A Genetic Algorithm (GA) based hybrid fuzzy logic control strategy is also developed to reduce the endpoint vibration of a flexible manipulator without sacrificing its speed of response. An uncoupled fuzzy logic controller approach is employed with individual controllers at the shoulder and the elbow link utilizing hub-angle error and hub-velocity feedback. GA has been used to extract and optimize the rule base of the fuzzy logic controller. The fitness function of GA optimization process is formed by taking weighted sum of multiple objectives to trade off between system overshoot and rise time. Moreover, scaling factors of the fuzzy controller are tuned with GA to improve the performance of the controller. A significant amount of vibration reduction has been achieved with satisfactory level of overshoot, rise time and settling time and steady state error.