Acquisition of the contact force at the instrument tip can enable better performance, e.g. transparency of the haptic feedback in the surgical robot systems. It is, however, difficult to measure the contact force directly due to technical limitations in attaching sensors to the tip of the instruments. This paper proposes a method to estimate the forces by installing the sensors away from the instrument tip. The proposed method employs specially designed mechanical parts of the slave robot, i.e. a slider cover plate for the z-axis translational force along the insertion direction, and docking clamps for the rotational pivot torques around the fulcrum point. Strain gauges are attached to specially designed places with enhancing shapes. The simulation results of the force estimation are presented to confirm the strain concentration area. The proposed method is validated with quantitative experimental results. Calibrated weights are determined upon the comparison of the strain value with a calibrated 6-axis force/torque sensor. The percentage error in the force calibration is about 5 similar to 8% calculated by the root mean square error (RMSE) of force-sensing performance. In addition, it can be computed by considering only the bending phase of each sensor although the hysteresis is observed from the calibration graph.