Recently, attention has been paid to pushing task by robots. A flexible mobile robot with a spring was devised to achieve safe contact during the pushing task. In this paper, two types of pushing task were assumed, one is pushing a fixed object and second is pushing a mobile object. A control law for flexible mobile robots to perform these tasks was proposed. The first is resonance ratio control for force control on a fixed object. Second, deceleration time adjustment method was proposed to carry mobile object without overrunning the target position. Also an observer to estimate friction was proposed, which is an index for adapting deceleration time. The performance of the proposed methods ware verified by simulation.