Objective: In this work we address limitations in state-of-the-art ultrasound robots by designing and integrating a novel soft robotic system for ultrasound imaging. It employs the inherent qualities of soft fluidic actuators to establish safe, adaptable interaction between ultrasound probe and patient. Methods: We acquire clinical data to determine the movement ranges and force levels required in prenatal foetal ultrasound imaging and design the soft robotic end-effector accordingly. We verify its mechanical characteristics, derive and validate a kinetostatic model and demonstrate controllability and imaging capabilities on an ultrasound phantom. Results: The soft robot exhibits the desired stiffness characteristics and is able to reach 100% of the required workspace when no external force is present, and 95% of the workspace when considering its compliance. The model can accurately predict the end-effector pose with a mean error of 1.18+/-0.29mm in position and 0.92+/-0.47deg in orientation. The derived controller is, with an average position error of 0.39mm, able to track a target pose efficiently without and with externally applied loads. Ultrasound images acquired with the system are of equally good quality compared to a manual sonographer scan. Conclusion: The system is able to withstand loads commonly applied during foetal ultrasound scans and remains controllable with a motion range similar to manual scanning. Significance: The proposed soft robot presents a safe, cost-effective solution to offloading sonographers in day-to-day scanning routines. The design and modelling paradigms are greatly generalizable and particularly suitable for designing soft robots for physical interaction tasks.