In this article, a path planning algorithm for nonholonomic mobile flexible manipulators is presented that computes the robot trajectory by maximizing pose stability measures. Zero moment point criterion is used as a performance index for the system stability, which regards the mass moment of inertia of the mobile base. In dynamic analysis, an efficient model is employed to describe the treatment of flexible structure, in which both the geometric elastic nonlinearity and the foreshortening effects are considered. The optimization strategy is based on the indirect solution of the open-loop optimal control problem. Necessary optimality conditions in the form of Pontryagin’s minimum principle are established, which leads to a standard form of a two-point boundary value problem. A new objective function is proposed to improve stability for mobile flexible robot. In order to initially check the validity of the dynamic equations, the proposed model has been implemented and tested on a fixed-base flexible arm undergoing large deflection. A simulation study has been carried out to investigate further the validity and effectiveness of the mobile flexible manipulators on finding the optimal path between two points with stability consideration. The results clearly show the effect of flexibility and tip over stability on the mobile manipulators.