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Back injuries are the most prevalent work-related musculoskeletal disorders and represent a major cause of disability and socio-economic problems. Although innovations in wearable robots aim to alleviate this hazard, the majority of existing exoskeletons are obtrusive because the rigid linkage design limits natural movement, thus causing ergonomic risk. Moreover, these existing systems are typically only suitable for one type of movement assistance, not ubiquitous for a wide variety of activities. To fill in this gap, this paper presents a new wearable robot design approach continuum soft exoskeleton. This wearable robot is unobtrusive and assists both squat and stoops while not impeding walking motion. To tackle the challenge of the unique anatomy of spine, our robot is conformal to human anatomy and it can reduce multiple types of forces along the human spine such as the spinae muscle force, shear, and compression force of the lumbar vertebrae. We derived kinematics and kinetics models of this mechanism and established an analytical biomechanics model of human-robot interaction. Quantitative analysis of disc compression force, disc shear force and muscle force was performed in simulation. We further developed a virtual impedance control strategy to deliver force control and compensate hysteresis of Bowden cable transmission. The feasibility of the prototype was experimentally tested on three healthy subjects. The root mean square error of force tracking is 6.63 N (3.3 % of the 200N peak force) and it demonstrated that it can actively control the stiffness to the desired value. This continuum soft exoskeleton represents a feasible solution with the potential to reduce back pain for multiple activities and multiple forces along the human spine.