A robotic surgical system includes a surgical instrument and a processor. The surgical instrument includes an elongate hollow shaft having a flexible section, a sensor apparatus configured to generate sensor data about the flexible section, and a force transmission mechanism coupled to the proximal end of the shaft. The processor is communicatively coupled to the sensor apparatus. The processor is configured to receive the sensor data about the flexible section from the sensor apparatus and to combine the sensor data received from the sensor apparatus with known information regarding mechanical and material property data for the surgical instrument to derive at least one of an internal actuation force applied by the force transmission mechanism or external force information for the surgical instrument.