Recently, much attention due to the wide range of applications has been given to the mobile robot. Considering that the mobile robots are covered a wide workspace are huge interest. Because the energy consumption of the motors are directly proportional to the mass and size of the elements of robot, links of robots with long and light are used. In this case link has a deformation, that can not be ignored. Rigid robot is heavy, bulky and has low speed and high power consumption, while the elastic robot due to the greater reliability, smaller size, higher efficiency, lower production cost, greater mobility and high speed has more advantage than rigid robot. The mobile robot is used in this research consists of a two-part elastic arm, which includes revolute joints. Both of the links of this manipulator are considered elastic and the robot is moved on the horizontal plane. In the present research, open-loop optimal control method is proposed as an approach for trajectory optimization of flexible mobile manipulator for a given two-end-point task in point-to-point motion. Equations of motion of the mobile robot are obtained by Lagrangian method. Then, the assumed modes method is used to obtain a model with limited degrees of freedom. Kinematic model is established based on the standard frame transformation matrices that includes rigid rotations and elastic displacements by assuming that they are small. Book modified method is used to obtain kinematic elastic links. Elastic manipulator links are modeled as Euler-Bernoulli beams with clamped-mass boundary conditions. Non-holonomic constraint and additional kinematic constraints are considered in order to specify the base motion. Performance criterion that includes the square of the angular velocity and joint torque is introduced. The torque and velocity are determined to minimize the performance criterion. Optimal control problem is converted into a two point boundary value problem by using the calculus of variations and the Hamiltonian function and then Pontryagin’s minimum principle is used. By considering the different weight coefficients for angular velocity joints and the torque on the joints of the robot in the performance criterion, effect of weight coefficients are investigated on the solution. Finally, the flexible arm with mobile base is simulated to illustrate the ability of this method. MATLAB software is used to solve the equations. The results are compared with results from other papers to prove the correct the dynamic model. The results are shown that increasing the weight ratio of the joint angular velocity in the performance criterion, angular position is changed approximately to a straight line, range of joints angular velocity is decreased and torque is raised at the beginning and end of the path. Keywords: Mobile robot, Optimal control, Flexible link, Trajectory planning